# Group divisible designs with block size five: direct constructions

A. D. Forbes  LSBU Business School, London South Bank University, 103 Borough
Road, London SE1 0AA, UK<EMAIL_ADDRESS>
(Date: version 2.1 )

###### Abstract.

We give direct constructions for 233 group divisible designs with block size
five, mostly of type $g^{u}m^{1}$, $m>0$.

###### Key words and phrases:

Group divisible design, 5-GDD

###### 2010 Mathematics Subject Classification:

05B30

##  1\. Introduction

For our purpose, a group divisible design with block size 5, $5$-GDD, and type
$g_{1}^{u_{1}}g_{2}^{u_{2}}\dots g_{r}^{u_{r}}$ is an ordered triple
($V,\mathcal{G},\mathcal{B}$) such that:

  1. (i)

$V$ is a base set of cardinality $u_{1}g_{1}+u_{2}g_{2}+\dots+u_{r}g_{r}$;

  2. (ii)

$\mathcal{G}$ is a partition of $V$ into $u_{i}$ subsets of cardinality
$g_{i}$, $i=1,2,\dots,r$, called groups;

  3. (iii)

$\mathcal{B}$ is a non-empty collection of 5-subsets of $V$ called blocks; and

  4. (iv)

each pair of elements from distinct groups occurs in precisely one block but
no pair of elements from the same group occurs in any block.

The sole purpose of this paper is to prove Theorem 1.1, below, which asserts
the existence of 233 specific 5-GDDs. Direct constructions are given in each
case, but it is possible that some might arise from known structures. The
paper is cited by [1] to which it is intended to act as a supplement. We hope
it will be of some use to researchers.

######  Theorem 1.1.

There exist $5$-$\mathrm{GDD}$s of types $1^{48}9^{1}$, $1^{60}9^{1}$,
$1^{60}13^{1}$, $1^{68}9^{1}$, $1^{72}17^{1}$, $1^{80}9^{1}$, $1^{80}13^{1}$,
$1^{80}25^{1}$, $1^{84}21^{1}$, $1^{88}9^{1}$, $1^{92}17^{1}$, $1^{96}25^{1}$,
$1^{100}9^{1}$, $1^{100}13^{1}$, $1^{100}25^{1}$, $1^{104}21^{1}$,
$1^{108}9^{1}$, $1^{108}29^{1}$, $1^{112}17^{1}$, $1^{124}21^{1}$,
$1^{128}9^{1}$, $1^{128}29^{1}$, $1^{132}17^{1}$, $1^{132}37^{1}$,
$1^{136}25^{1}$, $1^{144}21^{1}$, $1^{144}41^{1}$, $1^{148}29^{1}$,
$1^{152}17^{1}$, $1^{152}37^{1}$, $1^{156}25^{1}$, $1^{156}45^{1}$,
$1^{160}33^{1}$, $1^{164}21^{1}$, $1^{164}41^{1}$, $1^{168}29^{1}$,
$1^{168}49^{1}$, $1^{172}17^{1}$, $1^{176}25^{1}$, $1^{176}45^{1}$,
$1^{184}21^{1}$, $1^{184}41^{1}$, $1^{188}29^{1}$, $1^{192}17^{1}$,
$1^{192}37^{1}$, $1^{192}57^{1}$, $1^{196}25^{1}$, $1^{196}45^{1}$,
$2^{32}14^{1}$, $2^{40}6^{1}$, $2^{48}18^{1}$, $2^{52}14^{1}$, $2^{56}10^{1}$,
$2^{60}6^{1}$, $3^{20}11^{1}$, $3^{28}7^{1}$, $3^{32}11^{1}$, $3^{36}15^{1}$,
$5^{24}25^{1}$, $5^{28}25^{1}$, $5^{32}25^{1}$, $5^{32}45^{1}$,
$5^{36}45^{1}$, $5^{40}45^{1}$, $5^{44}25^{1}$, $5^{44}45^{1}$,
$6^{16}10^{1}$, $8^{8}12^{1}$, $8^{10}16^{1}$, $8^{10}20^{1}$, $8^{14}28^{1}$,
$8^{15}4^{1}$, $8^{15}16^{1}$, $8^{15}24^{1}$, $8^{15}36^{1}$, $8^{16}20^{1}$,
$8^{17}16^{1}$, $8^{18}32^{1}$, $8^{20}44^{1}$, $8^{21}20^{1}$,
$8^{21}40^{1}$, $8^{22}16^{1}$, $8^{22}36^{1}$, $8^{23}32^{1}$,
$8^{24}28^{1}$, $8^{25}4^{1}$, $8^{25}24^{1}$, $8^{26}20^{1}$, $8^{27}16^{1}$,
$8^{28}12^{1}$, $9^{8}1^{1}$, $9^{12}13^{1}$, $9^{16}5^{1}$, $9^{16}25^{1}$,
$9^{20}17^{1}$, $9^{20}29^{1}$, $9^{20}37^{1}$, $9^{20}49^{1}$, $9^{28}1^{1}$,
$10^{10}18^{1}$, $10^{20}38^{1}$, $11^{20}19^{1}$, $12^{5}8^{1}$,
$12^{10}8^{1}$, $12^{10}16^{1}$, $12^{10}28^{1}$, $12^{11}20^{1}$,
$12^{12}4^{1}$, $12^{12}24^{1}$, $12^{13}8^{1}$, $12^{13}28^{1}$,
$12^{14}32^{1}$, $12^{15}8^{1}$, $12^{15}16^{1}$, $12^{15}28^{1}$,
$12^{15}36^{1}$, $12^{15}48^{1}$, $12^{16}20^{1}$, $12^{16}40^{1}$,
$12^{17}4^{1}$, $12^{17}24^{1}$, $12^{17}44^{1}$, $12^{18}8^{1}$,
$12^{18}28^{1}$, $12^{18}48^{1}$, $12^{19}32^{1}$, $12^{19}52^{1}$,
$12^{20}8^{1}$, $12^{21}20^{1}$, $12^{21}40^{1}$, $12^{21}60^{1}$,
$12^{22}4^{1}$, $12^{22}24^{1}$, $12^{22}44^{1}$, $12^{22}64^{1}$,
$12^{23}28^{1}$, $12^{23}48^{1}$, $12^{23}68^{1}$, $12^{24}32^{1}$,
$12^{24}52^{1}$, $12^{27}4^{1}$, $13^{8}17^{1}$, $13^{12}1^{1}$,
$13^{12}21^{1}$, $13^{12}41^{1}$, $13^{16}5^{1}$, $13^{16}25^{1}$,
$13^{20}1^{1}$, $14^{8}6^{1}$, $16^{6}20^{1}$, $16^{7}12^{1}$, $16^{8}4^{1}$,
$16^{9}36^{1}$, $16^{10}8^{1}$, $16^{10}20^{1}$, $16^{10}28^{1}$,
$16^{10}36^{1}$, $16^{10}40^{1}$, $16^{11}20^{1}$, $16^{11}40^{1}$,
$16^{12}12^{1}$, $16^{12}52^{1}$, $16^{13}4^{1}$, $16^{13}24^{1}$,
$16^{13}44^{1}$, $16^{14}36^{1}$, $16^{15}8^{1}$, $16^{15}28^{1}$,
$16^{16}20^{1}$, $16^{16}40^{1}$, $16^{17}12^{1}$, $17^{8}13^{1}$,
$17^{8}33^{1}$, $17^{12}9^{1}$, $17^{12}29^{1}$, $17^{12}49^{1}$,
$17^{16}5^{1}$, $20^{8}40^{1}$, $20^{9}40^{1}$, $20^{10}36^{1}$,
$20^{10}40^{1}$, $20^{11}40^{1}$, $21^{8}9^{1}$, $21^{8}29^{1}$,
$21^{12}17^{1}$, $23^{8}7^{1}$, $24^{6}20^{1}$, $24^{7}8^{1}$, $24^{7}28^{1}$,
$24^{8}16^{1}$, $24^{8}36^{1}$, $24^{9}4^{1}$, $24^{9}44^{1}$, $24^{10}4^{1}$,
$24^{10}12^{1}$, $24^{10}32^{1}$, $24^{11}20^{1}$, $25^{8}5^{1}$,
$25^{8}45^{1}$, $28^{6}20^{1}$, $28^{6}40^{1}$, $28^{7}16^{1}$,
$28^{7}36^{1}$, $28^{8}12^{1}$, $28^{8}32^{1}$, $28^{8}52^{1}$, $28^{9}8^{1}$,
$28^{9}48^{1}$, $28^{10}4^{1}$, $28^{10}24^{1}$, $29^{8}1^{1}$,
$29^{8}21^{1}$, $32^{6}20^{1}$, $32^{6}40^{1}$, $32^{7}4^{1}$, $32^{7}24^{1}$,
$32^{7}44^{1}$, $32^{8}8^{1}$, $32^{8}28^{1}$, $32^{9}12^{1}$, $36^{6}20^{1}$,
$36^{6}40^{1}$, $36^{7}12^{1}$, $36^{7}32^{1}$, $36^{8}24^{1}$,
$40^{6}20^{1}$, $44^{6}20^{1}$, $44^{6}40^{1}$, $44^{7}8^{1}$, $48^{6}20^{1}$,
$1^{16}9^{5}$, $1^{46}5^{3}$ and $4^{5}8^{5}$.

###### Proof.

$1^{48}9^{1}$ With the point set $\\{0,1,\dots,56\\}$ partitioned into residue
classes modulo $48$ for $\\{0,1,\dots,47\\}$, and $\\{48,49,\dots,56\\}$, the
design is generated from

$\\{0,1,3,11,32\\}$, $\\{0,4,18,43,52\\}$, $\\{0,6,13,28,51\\}$,

$\\{0,12,24,36,56\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}48)$ for $x<48$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+48$ for $48\leq x<56$, $56\mapsto 56$,
$0\leq j<48$ for the first three blocks, $0\leq j<12$ for the last block.
[(57, ((3, 48, ((48, 1), (8, 1), (1, 1))), (1, 12, ((48, 1), (8, 1), (1,
1)))), ((1, 48), (9, 1)))]

$1^{60}9^{1}$ With the point set $\\{0,1,\dots,68\\}$ partitioned into residue
classes modulo $60$ for $\\{0,1,\dots,59\\}$, and $\\{60,61,\dots,68\\}$, the
design is generated from

$\\{0,1,7,58,66\\}$, $\\{0,5,39,41,44\\}$, $\\{0,8,31,43,59\\}$,

$\\{0,4,17,37,50\\}$, $\\{0,11,22,42,60\\}$, $\\{0,6,25,32,62\\}$,

$\\{1,5,15,23,65\\}$, $\\{0,15,30,45,68\\}$, $\\{0,12,24,36,48\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}60)$ for $x<60$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}6))+60$ for $60\leq x<66$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+66$ for $66\leq x<68$, $68\mapsto 68$,
$0\leq j<30$ for the first seven blocks, $0\leq j<15$ for the next block,
$0\leq j<6$ for the last block.
[(69, ((7, 30, ((60, 2), (6, 1), (2, 1), (1, 1))), (1, 15, ((60, 2), (6, 1),
(2, 1), (1, 1))), (1, 6, ((60, 2), (6, 1), (2, 1), (1, 1)))), ((1, 60), (9,
1)))]

$1^{60}13^{1}$ With the point set $\\{0,1,\dots,72\\}$ partitioned into
residue classes modulo $60$ for $\\{0,1,\dots,59\\}$, and
$\\{60,61,\dots,72\\}$, the design is generated from

$\\{0,2,34,59,61\\}$, $\\{0,10,21,23,67\\}$, $\\{0,1,35,41,65\\}$,

$\\{0,3,12,19,55\\}$, $\\{0,5,16,36,53\\}$, $\\{0,6,39,52,66\\}$,

$\\{0,4,22,31,68\\}$, $\\{1,5,15,43,60\\}$, $\\{0,15,30,45,72\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}60)$ for $x<60$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}12))+60$ for $60\leq x<72$, $72\mapsto 72$,
$0\leq j<30$ for the first eight blocks, $0\leq j<15$ for the last block.
[(73, ((8, 30, ((60, 2), (12, 2), (1, 1))), (1, 15, ((60, 2), (12, 2), (1,
1)))), ((1, 60), (13, 1)))]

$1^{68}9^{1}$ With the point set $\\{0,1,\dots,76\\}$ partitioned into residue
classes modulo $68$ for $\\{0,1,\dots,67\\}$, and $\\{68,69,\dots,76\\}$, the
design is generated from

$\\{0,1,7,66,69\\}$, $\\{0,5,15,62,71\\}$, $\\{0,10,41,67,70\\}$,

$\\{0,19,33,38,68\\}$, $\\{0,4,12,26,44\\}$, $\\{0,20,43,55,59\\}$,

$\\{0,25,27,47,65\\}$, $\\{0,13,37,45,52\\}$, $\\{0,17,34,51,76\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}68)$ for $x<68$,
$x\mapsto(x-68+4j~{}(\mathrm{mod}~{}8))+68$ for $68\leq x<76$, $76\mapsto 76$,
$0\leq j<34$ for the first eight blocks, $0\leq j<17$ for the last block.
[(77, ((8, 34, ((68, 2), (8, 4), (1, 1))), (1, 17, ((68, 2), (8, 4), (1,
1)))), ((1, 68), (9, 1)))]

$1^{72}17^{1}$ With the point set $\\{0,1,\dots,88\\}$ partitioned into
residue classes modulo $72$ for $\\{0,1,\dots,71\\}$, and
$\\{72,73,\dots,88\\}$, the design is generated from

$\\{0,1,3,66,84\\}$, $\\{0,5,17,27,51\\}$, $\\{0,8,39,52,76\\}$,

$\\{0,14,30,49,83\\}$, $\\{0,4,15,47,78\\}$, $\\{0,18,36,54,88\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}72)$ for $x<72$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+72$ for $72\leq x<84$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+84$ for $84\leq x<88$, $88\mapsto 88$,
$0\leq j<72$ for the first five blocks, $0\leq j<18$ for the last block.
[(89, ((5, 72, ((72, 1), (12, 1), (4, 1), (1, 1))), (1, 18, ((72, 1), (12, 1),
(4, 1), (1, 1)))), ((1, 72), (17, 1)))]

$1^{80}9^{1}$ With the point set $\\{0,1,\dots,88\\}$ partitioned into residue
classes modulo $80$ for $\\{0,1,\dots,79\\}$, and $\\{80,81,\dots,88\\}$, the
design is generated from

$\\{0,47,51,59,80\\}$, $\\{0,1,74,78,82\\}$, $\\{0,5,19,70,87\\}$,

$\\{0,21,45,58,86\\}$, $\\{0,8,34,65,71\\}$, $\\{0,9,35,62,79\\}$,

$\\{0,12,25,36,50\\}$, $\\{0,11,33,49,52\\}$, $\\{0,23,41,73,75\\}$,

$\\{0,20,40,60,88\\}$, $\\{1,21,41,61,88\\}$, $\\{0,16,32,48,64\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+80$ for $80\leq x<88$, $88\mapsto 88$,
$0\leq j<40$ for the first nine blocks, $0\leq j<10$ for the next two blocks,
$0\leq j<8$ for the last block.
[(89, ((9, 40, ((80, 2), (8, 1), (1, 1))), (2, 10, ((80, 2), (8, 1), (1, 1))),
(1, 8, ((80, 2), (8, 1), (1, 1)))), ((1, 80), (9, 1)))]

$1^{80}13^{1}$ With the point set $\\{0,1,\dots,92\\}$ partitioned into
residue classes modulo $80$ for $\\{0,1,\dots,79\\}$, and
$\\{80,81,\dots,92\\}$, the design is generated from

$\\{0,1,3,74,88\\}$, $\\{0,4,21,47,52\\}$, $\\{0,8,22,35,64\\}$,

$\\{0,10,46,65,82\\}$, $\\{0,11,23,41,86\\}$, $\\{0,20,40,60,92\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+80$ for $80\leq x<88$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+88$ for $88\leq x<92$, $92\mapsto 92$,
$0\leq j<80$ for the first five blocks, $0\leq j<20$ for the last block.
[(93, ((5, 80, ((80, 1), (8, 1), (4, 1), (1, 1))), (1, 20, ((80, 1), (8, 1),
(4, 1), (1, 1)))), ((1, 80), (13, 1)))]

$1^{80}25^{1}$ With the point set $\\{0,1,\dots,104\\}$ partitioned into
residue classes modulo $80$ for $\\{0,1,\dots,79\\}$, and
$\\{80,81,\dots,104\\}$, the design is generated from

$\\{0,5,38,49,98\\}$, $\\{0,1,4,23,102\\}$, $\\{0,6,52,73,96\\}$,

$\\{0,9,26,50,91\\}$, $\\{0,2,14,29,88\\}$, $\\{0,8,18,43,95\\}$,

$\\{0,20,40,60,100\\}$, $\\{0,16,32,48,64\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+80$ for $80\leq x<100$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}5))+100$ for $x\geq 100$, $0\leq j<80$ for the
first six blocks, $0\leq j<20$ for the next block, $0\leq j<16$ for the last
block.
[(105, ((6, 80, ((80, 1), (20, 1), (5, 1))), (1, 20, ((80, 1), (20, 1), (5,
1))), (1, 16, ((80, 1), (20, 1), (5, 1)))), ((1, 80), (25, 1)))]

$1^{84}21^{1}$ With the point set $\\{0,1,\dots,104\\}$ partitioned into
residue classes modulo $84$ for $\\{0,1,\dots,83\\}$, and
$\\{84,85,\dots,104\\}$, the design is generated from

$\\{0,1,4,6,91\\}$, $\\{0,7,15,29,96\\}$, $\\{0,9,28,40,60\\}$,

$\\{0,11,37,54,94\\}$, $\\{0,10,35,48,86\\}$, $\\{0,16,39,66,95\\}$,

$\\{0,21,42,63,84\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}84)$ for $x<84$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}21))+84$ for $x\geq 84$, $0\leq j<84$ for the
first six blocks, $0\leq j<21$ for the last block.
[(105, ((6, 84, ((84, 1), (21, 1))), (1, 21, ((84, 1), (21, 1)))), ((1, 84),
(21, 1)))]

$1^{88}9^{1}$ With the point set $\\{0,1,\dots,96\\}$ partitioned into residue
classes modulo $88$ for $\\{0,1,\dots,87\\}$, and $\\{88,89,\dots,96\\}$, the
design is generated from

$\\{0,1,3,11,15\\}$, $\\{0,7,23,42,63\\}$, $\\{0,9,27,47,64\\}$,

$\\{0,5,31,59,88\\}$, $\\{0,6,45,58,92\\}$, $\\{0,22,44,66,96\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}88)$ for $x<88$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+88$ for $88\leq x<96$, $96\mapsto 96$,
$0\leq j<88$ for the first five blocks, $0\leq j<22$ for the last block.
[(97, ((5, 88, ((88, 1), (8, 1), (1, 1))), (1, 22, ((88, 1), (8, 1), (1,
1)))), ((1, 88), (9, 1)))]

$1^{92}17^{1}$ With the point set $\\{0,1,\dots,108\\}$ partitioned into
residue classes modulo $92$ for $\\{0,1,\dots,91\\}$, and
$\\{92,93,\dots,108\\}$, the design is generated from

$\\{65,107,64,78,59\\}$, $\\{102,21,10,51,48\\}$, $\\{51,44,104,53,54\\}$,

$\\{71,97,29,0,86\\}$, $\\{0,2,15,49,95\\}$, $\\{0,17,34,55,98\\}$,

$\\{0,18,51,61,92\\}$, $\\{0,25,39,50,93\\}$, $\\{0,5,31,40,70\\}$,

$\\{0,4,16,64,72\\}$, $\\{0,19,37,59,66\\}$, $\\{1,5,17,65,73\\}$,

$\\{0,23,46,69,108\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}92)$ for $x<92$,
$x\mapsto(x-92+8j~{}(\mathrm{mod}~{}16))+92$ for $92\leq x<108$, $108\mapsto
108$, $0\leq j<46$ for the first 12 blocks, $0\leq j<23$ for the last block.
[(109, ((12, 46, ((92, 2), (16, 8), (1, 1))), (1, 23, ((92, 2), (16, 8), (1,
1)))), ((1, 92), (17, 1)))]

$1^{96}25^{1}$ With the point set $\\{0,1,\dots,120\\}$ partitioned into
residue classes modulo $96$ for $\\{0,1,\dots,95\\}$, and
$\\{96,97,\dots,120\\}$, the design is generated from

$\\{44,80,52,55,98\\}$, $\\{100,72,73,11,15\\}$, $\\{0,2,12,53,108\\}$,

$\\{0,6,15,80,101\\}$, $\\{0,7,21,40,104\\}$, $\\{0,13,30,67,111\\}$,

$\\{0,5,23,49,69\\}$, $\\{0,24,48,72,120\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}96)$ for $x<96$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+96$ for $96\leq x<120$, $120\mapsto 120$,
$0\leq j<96$ for the first seven blocks, $0\leq j<24$ for the last block.
[(121, ((7, 96, ((96, 1), (24, 1), (1, 1))), (1, 24, ((96, 1), (24, 1), (1,
1)))), ((1, 96), (25, 1)))]

$1^{100}9^{1}$ With the point set $\\{0,1,\dots,108\\}$ partitioned into
residue classes modulo $100$ for $\\{0,1,\dots,99\\}$, and
$\\{100,101,\dots,108\\}$, the design is generated from

$\\{53,101,75,76,18\\}$, $\\{30,96,11,92,43\\}$, $\\{75,64,103,38,29\\}$,

$\\{0,1,7,98,100\\}$, $\\{0,23,70,97,102\\}$, $\\{0,16,55,68,85\\}$,

$\\{0,5,33,44,93\\}$, $\\{0,6,14,24,78\\}$, $\\{0,12,43,79,95\\}$,

$\\{0,29,63,71,73\\}$, $\\{0,21,41,45,59\\}$, $\\{0,25,50,75,108\\}$,

$\\{0,20,40,60,80\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}100)$ for $x<100$,
$x\mapsto(x-100+4j~{}(\mathrm{mod}~{}8))+100$ for $100\leq x<108$, $108\mapsto
108$, $0\leq j<50$ for the first 11 blocks, $0\leq j<25$ for the next block,
$0\leq j<10$ for the last block.
[(109, ((11, 50, ((100, 2), (8, 4), (1, 1))), (1, 25, ((100, 2), (8, 4), (1,
1))), (1, 10, ((100, 2), (8, 4), (1, 1)))), ((1, 100), (9, 1)))]

$1^{100}13^{1}$ With the point set $\\{0,1,\dots,112\\}$ partitioned into
residue classes modulo $100$ for $\\{0,1,\dots,99\\}$, and
$\\{100,101,\dots,112\\}$, the design is generated from

$\\{107,32,94,3,9\\}$, $\\{5,105,91,32,10\\}$, $\\{0,1,43,46,100\\}$,

$\\{0,2,10,26,66\\}$, $\\{0,4,32,53,65\\}$, $\\{0,7,18,70,87\\}$,

$\\{0,25,50,75,112\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}100)$ for $x<100$,
$x\mapsto(x-100+3j~{}(\mathrm{mod}~{}12))+100$ for $100\leq x<112$,
$112\mapsto 112$, $0\leq j<100$ for the first six blocks, $0\leq j<25$ for the
last block.
[(113, ((6, 100, ((100, 1), (12, 3), (1, 1))), (1, 25, ((100, 1), (12, 3), (1,
1)))), ((1, 100), (13, 1)))]

$1^{100}25^{1}$ With the point set $\\{0,1,\dots,124\\}$ partitioned into
residue classes modulo $100$ for $\\{0,1,\dots,99\\}$, and
$\\{100,101,\dots,124\\}$, the design is generated from

$\\{104,90,92,3,36\\}$, $\\{49,71,13,97,103\\}$, $\\{0,1,6,83,111\\}$,

$\\{0,9,43,90,117\\}$, $\\{0,7,15,45,86\\}$, $\\{0,12,39,63,109\\}$,

$\\{0,3,68,72,116\\}$, $\\{0,25,50,75,100\\}$, $\\{0,20,40,60,80\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}100)$ for $x<100$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}25))+100$ for $x\geq 100$, $0\leq j<100$ for
the first seven blocks, $0\leq j<25$ for the next block, $0\leq j<20$ for the
last block.
[(125, ((7, 100, ((100, 1), (25, 1))), (1, 25, ((100, 1), (25, 1))), (1, 20,
((100, 1), (25, 1)))), ((1, 100), (25, 1)))]

$1^{104}21^{1}$ With the point set $\\{0,1,\dots,124\\}$ partitioned into
residue classes modulo $104$ for $\\{0,1,\dots,103\\}$, and
$\\{104,105,\dots,124\\}$, the design is generated from

$\\{22,57,113,43,56\\}$, $\\{56,121,102,71,93\\}$, $\\{0,2,5,43,105\\}$,

$\\{0,7,25,54,107\\}$, $\\{0,11,30,53,104\\}$, $\\{0,6,16,33,65\\}$,

$\\{0,4,28,40,48\\}$, $\\{0,26,52,78,124\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}104)$ for $x<104$,
$x\mapsto(x-104+5j~{}(\mathrm{mod}~{}20))+104$ for $104\leq x<124$,
$124\mapsto 124$, $0\leq j<104$ for the first seven blocks, $0\leq j<26$ for
the last block.
[(125, ((7, 104, ((104, 1), (20, 5), (1, 1))), (1, 26, ((104, 1), (20, 5), (1,
1)))), ((1, 104), (21, 1)))]

$1^{108}9^{1}$ With the point set $\\{0,1,\dots,116\\}$ partitioned into
residue classes modulo $108$ for $\\{0,1,\dots,107\\}$, and
$\\{108,109,\dots,116\\}$, the design is generated from

$\\{83,81,102,40,111\\}$, $\\{69,60,98,112,47\\}$, $\\{0,1,5,31,49\\}$,

$\\{0,8,28,42,53\\}$, $\\{0,3,15,39,76\\}$, $\\{0,6,16,23,56\\}$,

$\\{0,27,54,81,116\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}108)$ for $x<108$,
$x\mapsto(x-108+2j~{}(\mathrm{mod}~{}8))+108$ for $108\leq x<116$, $116\mapsto
116$, $0\leq j<108$ for the first six blocks, $0\leq j<27$ for the last block.
[(117, ((6, 108, ((108, 1), (8, 2), (1, 1))), (1, 27, ((108, 1), (8, 2), (1,
1)))), ((1, 108), (9, 1)))]

$1^{108}29^{1}$ With the point set $\\{0,1,\dots,136\\}$ partitioned into
residue classes modulo $108$ for $\\{0,1,\dots,107\\}$, and
$\\{108,109,\dots,136\\}$, the design is generated from

$\\{37,103,12,124,30\\}$, $\\{98,55,126,104,53\\}$, $\\{76,127,71,102,105\\}$,

$\\{0,9,19,30,121\\}$, $\\{0,4,62,75,112\\}$, $\\{0,8,20,48,84\\}$,

$\\{0,1,15,56,114\\}$, $\\{0,16,39,86,119\\}$, $\\{0,27,54,81,136\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}108)$ for $x<108$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+108$ for $108\leq x<120$,
$x\mapsto(x-120+4j~{}(\mathrm{mod}~{}16))+120$ for $120\leq x<136$,
$136\mapsto 136$, $0\leq j<108$ for the first eight blocks, $0\leq j<27$ for
the last block.
[(137, ((8, 108, ((108, 1), (12, 1), (16, 4), (1, 1))), (1, 27, ((108, 1),
(12, 1), (16, 4), (1, 1)))), ((1, 108), (29, 1)))]

$1^{112}17^{1}$ With the point set $\\{0,1,\dots,128\\}$ partitioned into
residue classes modulo $112$ for $\\{0,1,\dots,111\\}$, and
$\\{112,113,\dots,128\\}$, the design is generated from

$\\{104,2,96,103,5\\}$, $\\{86,15,27,10,113\\}$, $\\{0,2,32,48,70\\}$,

$\\{0,4,19,69,115\\}$, $\\{0,6,45,85,122\\}$, $\\{0,20,51,75,124\\}$,

$\\{0,9,34,63,86\\}$, $\\{0,28,56,84,128\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}112)$ for $x<112$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+112$ for $112\leq x<128$, $128\mapsto
128$, $0\leq j<112$ for the first seven blocks, $0\leq j<28$ for the last
block.
[(129, ((7, 112, ((112, 1), (16, 1), (1, 1))), (1, 28, ((112, 1), (16, 1), (1,
1)))), ((1, 112), (17, 1)))]

$1^{124}21^{1}$ With the point set $\\{0,1,\dots,144\\}$ partitioned into
residue classes modulo $124$ for $\\{0,1,\dots,123\\}$, and
$\\{124,125,\dots,144\\}$, the design is generated from

$\\{64,23,66,136,117\\}$, $\\{122,16,125,119,9\\}$, $\\{0,1,6,35,124\\}$,

$\\{0,9,55,70,127\\}$, $\\{0,10,23,97,128\\}$, $\\{0,16,40,65,98\\}$,

$\\{0,17,39,77,96\\}$, $\\{0,4,36,48,56\\}$, $\\{0,31,62,93,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}124)$ for $x<124$,
$x\mapsto(x-124+5j~{}(\mathrm{mod}~{}20))+124$ for $124\leq x<144$,
$144\mapsto 144$, $0\leq j<124$ for the first eight blocks, $0\leq j<31$ for
the last block.
[(145, ((8, 124, ((124, 1), (20, 5), (1, 1))), (1, 31, ((124, 1), (20, 5), (1,
1)))), ((1, 124), (21, 1)))]

$1^{128}9^{1}$ With the point set $\\{0,1,\dots,136\\}$ partitioned into
residue classes modulo $128$ for $\\{0,1,\dots,127\\}$, and
$\\{128,129,\dots,136\\}$, the design is generated from

$\\{78,4,128,66,21\\}$, $\\{93,130,34,115,65\\}$, $\\{0,1,3,9,14\\}$,

$\\{0,7,34,44,82\\}$, $\\{0,4,25,67,102\\}$, $\\{0,15,33,56,85\\}$,

$\\{0,16,36,55,104\\}$, $\\{0,32,64,96,136\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}128)$ for $x<128$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+128$ for $128\leq x<136$, $136\mapsto
136$, $0\leq j<128$ for the first seven blocks, $0\leq j<32$ for the last
block.
[(137, ((7, 128, ((128, 1), (8, 1), (1, 1))), (1, 32, ((128, 1), (8, 1), (1,
1)))), ((1, 128), (9, 1)))]

$1^{128}29^{1}$ With the point set $\\{0,1,\dots,156\\}$ partitioned into
residue classes modulo $128$ for $\\{0,1,\dots,127\\}$, and
$\\{128,129,\dots,156\\}$, the design is generated from

$\\{61,62,89,145,71\\}$, $\\{120,53,89,11,128\\}$, $\\{100,104,21,133,124\\}$,

$\\{0,2,76,123,145\\}$, $\\{0,13,39,98,152\\}$, $\\{0,16,33,62,106\\}$,

$\\{0,14,51,72,130\\}$, $\\{0,3,11,68,116\\}$, $\\{0,6,41,94,140\\}$,

$\\{0,32,64,96,156\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}128)$ for $x<128$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+128$ for $128\leq x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+144$ for $144\leq x<152$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+152$ for $152\leq x<156$, $156\mapsto
156$, $0\leq j<128$ for the first nine blocks, $0\leq j<32$ for the last
block.
[(157, ((9, 128, ((128, 1), (16, 1), (8, 1), (4, 1), (1, 1))), (1, 32, ((128,
1), (16, 1), (8, 1), (4, 1), (1, 1)))), ((1, 128), (29, 1)))]

$1^{132}17^{1}$ With the point set $\\{0,1,\dots,148\\}$ partitioned into
residue classes modulo $132$ for $\\{0,1,\dots,131\\}$, and
$\\{132,133,\dots,148\\}$, the design is generated from

$\\{102,126,4,6,64\\}$, $\\{23,113,109,92,143\\}$, $\\{0,1,23,26,144\\}$,

$\\{0,6,37,55,84\\}$, $\\{0,7,20,35,88\\}$, $\\{0,8,73,100,141\\}$,

$\\{0,9,50,89,136\\}$, $\\{0,5,16,61,118\\}$, $\\{0,33,66,99,148\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}132)$ for $x<132$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+132$ for $132\leq x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+144$ for $144\leq x<148$, $148\mapsto
148$, $0\leq j<132$ for the first eight blocks, $0\leq j<33$ for the last
block.
[(149, ((8, 132, ((132, 1), (12, 1), (4, 1), (1, 1))), (1, 33, ((132, 1), (12,
1), (4, 1), (1, 1)))), ((1, 132), (17, 1)))]

$1^{132}37^{1}$ With the point set $\\{0,1,\dots,168\\}$ partitioned into
residue classes modulo $132$ for $\\{0,1,\dots,131\\}$, and
$\\{132,133,\dots,168\\}$, the design is generated from

$\\{29,49,145,109,99\\}$, $\\{4,108,123,2,10\\}$, $\\{158,73,72,131,30\\}$,

$\\{0,3,49,54,165\\}$, $\\{0,4,69,91,134\\}$, $\\{0,7,68,95,143\\}$,

$\\{0,12,30,115,137\\}$, $\\{0,21,57,97,148\\}$, $\\{0,9,32,116,155\\}$,

$\\{0,14,53,108,153\\}$, $\\{0,33,66,99,132\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}132)$ for $x<132$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}33))+132$ for $132\leq x<165$,
$x\mapsto(x-165+j~{}(\mathrm{mod}~{}4))+165$ for $x\geq 165$, $0\leq j<132$
for the first ten blocks, $0\leq j<33$ for the last block.
[(169, ((10, 132, ((132, 1), (33, 1), (4, 1))), (1, 33, ((132, 1), (33, 1),
(4, 1)))), ((1, 132), (37, 1)))]

$1^{136}25^{1}$ With the point set $\\{0,1,\dots,160\\}$ partitioned into
residue classes modulo $136$ for $\\{0,1,\dots,135\\}$, and
$\\{136,137,\dots,160\\}$, the design is generated from

$\\{148,103,109,12,19\\}$, $\\{146,51,29,87,14\\}$, $\\{0,1,10,134,148\\}$,

$\\{0,4,17,42,146\\}$, $\\{0,21,44,75,108\\}$, $\\{0,11,27,80,104\\}$,

$\\{0,8,26,55,96\\}$, $\\{0,20,50,85,153\\}$, $\\{0,5,62,122,150\\}$,

$\\{0,34,68,102,160\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}136)$ for $x<136$,
$x\mapsto(x-136+3j~{}(\mathrm{mod}~{}24))+136$ for $136\leq x<160$,
$160\mapsto 160$, $0\leq j<136$ for the first nine blocks, $0\leq j<34$ for
the last block.
[(161, ((9, 136, ((136, 1), (24, 3), (1, 1))), (1, 34, ((136, 1), (24, 3), (1,
1)))), ((1, 136), (25, 1)))]

$1^{144}21^{1}$ With the point set $\\{0,1,\dots,164\\}$ partitioned into
residue classes modulo $144$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,164\\}$, the design is generated from

$\\{125,72,112,120,11\\}$, $\\{50,107,33,138,88\\}$, $\\{0,22,132,86,112\\}$,

$\\{0,6,21,103,160\\}$, $\\{0,2,11,79,95\\}$, $\\{0,7,78,107,144\\}$,

$\\{0,4,18,63,158\\}$, $\\{0,1,25,28,148\\}$, $\\{0,10,33,102,151\\}$,

$\\{0,36,72,108,164\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+144$ for $144\leq x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+160$ for $160\leq x<164$, $164\mapsto
164$, $0\leq j<144$ for the first nine blocks, $0\leq j<36$ for the last
block.
[(165, ((9, 144, ((144, 1), (16, 1), (4, 1), (1, 1))), (1, 36, ((144, 1), (16,
1), (4, 1), (1, 1)))), ((1, 144), (21, 1)))]

$1^{144}41^{1}$ With the point set $\\{0,1,\dots,184\\}$ partitioned into
residue classes modulo $144$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,184\\}$, the design is generated from

$\\{147,45,1,70,38\\}$, $\\{26,166,4,38,99\\}$, $\\{175,93,117,94,53\\}$,

$\\{107,23,13,56,91\\}$, $\\{0,2,5,131,180\\}$, $\\{0,9,62,114,169\\}$,

$\\{0,4,21,67,172\\}$, $\\{0,6,96,124,171\\}$, $\\{0,8,27,65,152\\}$,

$\\{0,11,58,113,178\\}$, $\\{0,14,70,99,148\\}$, $\\{0,36,72,108,184\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+144$ for $144\leq x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+180$ for $180\leq x<184$, $184\mapsto
184$, $0\leq j<144$ for the first 11 blocks, $0\leq j<36$ for the last block.
[(185, ((11, 144, ((144, 1), (36, 1), (4, 1), (1, 1))), (1, 36, ((144, 1),
(36, 1), (4, 1), (1, 1)))), ((1, 144), (41, 1)))]

$1^{148}29^{1}$ With the point set $\\{0,1,\dots,176\\}$ partitioned into
residue classes modulo $148$ for $\\{0,1,\dots,147\\}$, and
$\\{148,149,\dots,176\\}$, the design is generated from

$\\{154,90,12,33,55\\}$, $\\{148,51,54,52,45\\}$, $\\{105,34,60,7,158\\}$,

$\\{0,5,19,30,149\\}$, $\\{0,10,41,75,152\\}$, $\\{0,15,33,82,153\\}$,

$\\{0,17,63,86,150\\}$, $\\{0,4,42,55,94\\}$, $\\{0,12,40,72,101\\}$,

$\\{0,8,24,44,92\\}$, $\\{0,37,74,111,176\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}148)$ for $x<148$,
$x\mapsto(x-148+7j~{}(\mathrm{mod}~{}28))+148$ for $148\leq x<176$,
$176\mapsto 176$, $0\leq j<148$ for the first ten blocks, $0\leq j<37$ for the
last block.
[(177, ((10, 148, ((148, 1), (28, 7), (1, 1))), (1, 37, ((148, 1), (28, 7),
(1, 1)))), ((1, 148), (29, 1)))]

$1^{152}17^{1}$ With the point set $\\{0,1,\dots,168\\}$ partitioned into
residue classes modulo $152$ for $\\{0,1,\dots,151\\}$, and
$\\{152,153,\dots,168\\}$, the design is generated from

$\\{83,55,96,53,38\\}$, $\\{31,4,131,165,78\\}$, $\\{64,68,152,31,9\\}$,

$\\{0,1,19,92,164\\}$, $\\{0,9,21,98,165\\}$, $\\{0,10,44,80,112\\}$,

$\\{0,7,31,88,117\\}$, $\\{0,3,8,14,104\\}$, $\\{0,16,39,65,85\\}$,

$\\{0,38,76,114,168\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}152)$ for $x<152$,
$x\mapsto(x-152+2j~{}(\mathrm{mod}~{}16))+152$ for $152\leq x<168$,
$168\mapsto 168$, $0\leq j<152$ for the first nine blocks, $0\leq j<38$ for
the last block.
[(169, ((9, 152, ((152, 1), (16, 2), (1, 1))), (1, 38, ((152, 1), (16, 2), (1,
1)))), ((1, 152), (17, 1)))]

$1^{152}37^{1}$ With the point set $\\{0,1,\dots,188\\}$ partitioned into
residue classes modulo $152$ for $\\{0,1,\dots,151\\}$, and
$\\{152,153,\dots,188\\}$, the design is generated from

$\\{181,146,57,149,84\\}$, $\\{72,115,154,82,101\\}$,
$\\{148,97,187,114,31\\}$,

$\\{82,7,166,137,52\\}$, $\\{0,1,5,58,157\\}$, $\\{0,8,24,49,64\\}$,

$\\{0,6,18,54,126\\}$, $\\{0,9,46,93,156\\}$, $\\{0,7,20,81,176\\}$,

$\\{0,11,42,124,171\\}$, $\\{0,2,23,102,175\\}$, $\\{0,38,76,114,188\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}152)$ for $x<152$,
$x\mapsto(x-152+4j~{}(\mathrm{mod}~{}32))+152$ for $152\leq x<184$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+184$ for $184\leq x<188$, $188\mapsto
188$, $0\leq j<152$ for the first 11 blocks, $0\leq j<38$ for the last block.
[(189, ((11, 152, ((152, 1), (32, 4), (4, 1), (1, 1))), (1, 38, ((152, 1),
(32, 4), (4, 1), (1, 1)))), ((1, 152), (37, 1)))]

$1^{156}25^{1}$ With the point set $\\{0,1,\dots,180\\}$ partitioned into
residue classes modulo $156$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,180\\}$, the design is generated from

$\\{32,117,8,74,57\\}$, $\\{125,55,33,85,113\\}$, $\\{41,103,40,175,114\\}$,

$\\{22,18,162,68,155\\}$, $\\{0,5,20,53,125\\}$, $\\{0,14,79,135,158\\}$,

$\\{0,27,61,115,162\\}$, $\\{0,3,9,16,127\\}$, $\\{0,18,55,130,171\\}$,

$\\{0,2,59,148,177\\}$, $\\{0,39,78,117,180\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x-156+2j~{}(\mathrm{mod}~{}24))+156$ for $156\leq x<180$,
$180\mapsto 180$, $0\leq j<156$ for the first ten blocks, $0\leq j<39$ for the
last block.
[(181, ((10, 156, ((156, 1), (24, 2), (1, 1))), (1, 39, ((156, 1), (24, 2),
(1, 1)))), ((1, 156), (25, 1)))]

$1^{156}45^{1}$ With the point set $\\{0,1,\dots,200\\}$ partitioned into
residue classes modulo $156$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,200\\}$, the design is generated from

$\\{155,128,193,57,154\\}$, $\\{177,141,110,95,97\\}$,
$\\{138,20,133,166,127\\}$,

$\\{194,85,104,127,34\\}$, $\\{80,84,62,183,117\\}$, $\\{0,10,99,131,162\\}$,

$\\{0,12,40,96,120\\}$, $\\{0,7,41,61,175\\}$, $\\{0,17,47,111,166\\}$,

$\\{0,8,29,81,185\\}$, $\\{0,3,90,106,173\\}$, $\\{0,9,77,91,167\\}$,

$\\{0,39,78,117,200\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x-156+3j~{}(\mathrm{mod}~{}36))+156$ for $156\leq x<192$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}8))+192$ for $192\leq x<200$, $200\mapsto
200$, $0\leq j<156$ for the first 12 blocks, $0\leq j<39$ for the last block.
[(201, ((12, 156, ((156, 1), (36, 3), (8, 2), (1, 1))), (1, 39, ((156, 1),
(36, 3), (8, 2), (1, 1)))), ((1, 156), (45, 1)))]

$1^{160}33^{1}$ With the point set $\\{0,1,\dots,192\\}$ partitioned into
residue classes modulo $160$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,192\\}$, the design is generated from

$\\{58,188,97,53,148\\}$, $\\{73,84,97,167,42\\}$, $\\{161,48,66,39,150\\}$,

$\\{17,151,5,161,51\\}$, $\\{0,1,75,79,184\\}$, $\\{0,7,61,104,172\\}$,

$\\{0,8,33,140,161\\}$, $\\{0,15,62,92,178\\}$, $\\{0,17,67,89,108\\}$,

$\\{0,3,32,38,48\\}$, $\\{0,2,23,59,96\\}$, $\\{0,40,80,120,192\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}32))+160$ for $160\leq x<192$, $192\mapsto
192$, $0\leq j<160$ for the first 11 blocks, $0\leq j<40$ for the last block.
[(193, ((11, 160, ((160, 1), (32, 1), (1, 1))), (1, 40, ((160, 1), (32, 1),
(1, 1)))), ((1, 160), (33, 1)))]

$1^{164}21^{1}$ With the point set $\\{0,1,\dots,184\\}$ partitioned into
residue classes modulo $164$ for $\\{0,1,\dots,163\\}$, and
$\\{164,165,\dots,184\\}$, the design is generated from

$\\{136,87,3,31,135\\}$, $\\{81,135,120,62,102\\}$, $\\{105,7,170,62,88\\}$,

$\\{0,2,71,77,168\\}$, $\\{0,9,46,99,167\\}$, $\\{0,10,23,117,164\\}$,

$\\{0,22,51,101,166\\}$, $\\{0,3,7,129,159\\}$, $\\{0,14,34,78,102\\}$,

$\\{0,11,27,72,139\\}$, $\\{0,41,82,123,184\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}164)$ for $x<164$,
$x\mapsto(x-164+5j~{}(\mathrm{mod}~{}20))+164$ for $164\leq x<184$,
$184\mapsto 184$, $0\leq j<164$ for the first ten blocks, $0\leq j<41$ for the
last block.
[(185, ((10, 164, ((164, 1), (20, 5), (1, 1))), (1, 41, ((164, 1), (20, 5),
(1, 1)))), ((1, 164), (21, 1)))]

$1^{164}41^{1}$ With the point set $\\{0,1,\dots,204\\}$ partitioned into
residue classes modulo $164$ for $\\{0,1,\dots,163\\}$, and
$\\{164,165,\dots,204\\}$, the design is generated from

$\\{19,76,176,22,45\\}$, $\\{78,201,25,7,88\\}$, $\\{145,106,203,55,72\\}$,

$\\{39,168,9,52,94\\}$, $\\{0,1,6,95,164\\}$, $\\{0,2,27,49,170\\}$,

$\\{0,7,21,126,165\\}$, $\\{0,9,67,86,169\\}$, $\\{0,11,46,61,172\\}$,

$\\{0,29,62,127,167\\}$, $\\{0,4,60,76,100\\}$, $\\{0,8,20,52,136\\}$,

$\\{0,41,82,123,204\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}164)$ for $x<164$,
$x\mapsto(x-164+10j~{}(\mathrm{mod}~{}40))+164$ for $164\leq x<204$,
$204\mapsto 204$, $0\leq j<164$ for the first 12 blocks, $0\leq j<41$ for the
last block.
[(205, ((12, 164, ((164, 1), (40, 10), (1, 1))), (1, 41, ((164, 1), (40, 10),
(1, 1)))), ((1, 164), (41, 1)))]

$1^{168}29^{1}$ With the point set $\\{0,1,\dots,196\\}$ partitioned into
residue classes modulo $168$ for $\\{0,1,\dots,167\\}$, and
$\\{168,169,\dots,196\\}$, the design is generated from

$\\{190,159,102,2,25\\}$, $\\{161,67,58,191,122\\}$, $\\{32,194,39,54,68\\}$,

$\\{20,65,137,25,163\\}$, $\\{0,1,4,62,148\\}$, $\\{0,10,28,88,115\\}$,

$\\{0,17,66,109,184\\}$, $\\{0,8,122,135,186\\}$, $\\{0,2,99,118,179\\}$,

$\\{0,6,37,130,175\\}$, $\\{0,12,47,79,95\\}$, $\\{0,42,84,126,196\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}168)$ for $x<168$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}28))+168$ for $168\leq x<196$, $196\mapsto
196$, $0\leq j<168$ for the first 11 blocks, $0\leq j<42$ for the last block.
[(197, ((11, 168, ((168, 1), (28, 1), (1, 1))), (1, 42, ((168, 1), (28, 1),
(1, 1)))), ((1, 168), (29, 1)))]

$1^{168}49^{1}$ With the point set $\\{0,1,\dots,216\\}$ partitioned into
residue classes modulo $168$ for $\\{0,1,\dots,167\\}$, and
$\\{168,169,\dots,216\\}$, the design is generated from

$\\{190,2,20,134,132\\}$, $\\{196,9,156,85,162\\}$, $\\{206,21,96,49,37\\}$,

$\\{121,134,68,209,36\\}$, $\\{39,158,84,169,157\\}$, $\\{0,3,141,146,194\\}$,

$\\{0,4,68,158,176\\}$, $\\{0,19,52,86,182\\}$, $\\{0,9,40,105,129\\}$,

$\\{0,8,43,69,215\\}$, $\\{0,7,51,62,211\\}$, $\\{0,17,46,127,209\\}$,

$\\{0,20,57,80,171\\}$, $\\{0,42,84,126,216\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}168)$ for $x<168$,
$x\mapsto(x-168+2j~{}(\mathrm{mod}~{}48))+168$ for $168\leq x<216$,
$216\mapsto 216$, $0\leq j<168$ for the first 13 blocks, $0\leq j<42$ for the
last block.
[(217, ((13, 168, ((168, 1), (48, 2), (1, 1))), (1, 42, ((168, 1), (48, 2),
(1, 1)))), ((1, 168), (49, 1)))]

$1^{172}17^{1}$ With the point set $\\{0,1,\dots,188\\}$ partitioned into
residue classes modulo $172$ for $\\{0,1,\dots,171\\}$, and
$\\{172,173,\dots,188\\}$, the design is generated from

$\\{91,84,164,53,31\\}$, $\\{113,19,59,8,56\\}$, $\\{136,163,111,144,8\\}$,

$\\{0,5,47,106,173\\}$, $\\{0,9,35,98,174\\}$, $\\{0,15,49,90,172\\}$,

$\\{0,21,79,102,175\\}$, $\\{0,1,46,96,108\\}$, $\\{0,13,29,85,117\\}$,

$\\{0,2,6,20,30\\}$, $\\{0,43,86,129,188\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}172)$ for $x<172$,
$x\mapsto(x-172+4j~{}(\mathrm{mod}~{}16))+172$ for $172\leq x<188$,
$188\mapsto 188$, $0\leq j<172$ for the first ten blocks, $0\leq j<43$ for the
last block.
[(189, ((10, 172, ((172, 1), (16, 4), (1, 1))), (1, 43, ((172, 1), (16, 4),
(1, 1)))), ((1, 172), (17, 1)))]

$1^{176}25^{1}$ With the point set $\\{0,1,\dots,200\\}$ partitioned into
residue classes modulo $176$ for $\\{0,1,\dots,175\\}$, and
$\\{176,177,\dots,200\\}$, the design is generated from

$\\{0,124,140,112,161\\}$, $\\{109,53,180,51,106\\}$,
$\\{173,103,10,125,84\\}$,

$\\{137,45,0,171,99\\}$, $\\{0,1,30,97,101\\}$, $\\{0,7,32,117,143\\}$,

$\\{0,9,23,69,193\\}$, $\\{0,11,31,73,198\\}$, $\\{0,6,63,158,178\\}$,

$\\{0,10,108,159,181\\}$, $\\{0,8,43,90,184\\}$, $\\{0,44,88,132,200\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}176)$ for $x<176$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+176$ for $176\leq x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+192$ for $192\leq x<200$, $200\mapsto
200$, $0\leq j<176$ for the first 11 blocks, $0\leq j<44$ for the last block.
[(201, ((11, 176, ((176, 1), (16, 1), (8, 1), (1, 1))), (1, 44, ((176, 1),
(16, 1), (8, 1), (1, 1)))), ((1, 176), (25, 1)))]

$1^{176}45^{1}$ With the point set $\\{0,1,\dots,220\\}$ partitioned into
residue classes modulo $176$ for $\\{0,1,\dots,175\\}$, and
$\\{176,177,\dots,220\\}$, the design is generated from

$\\{187,128,49,139,167\\}$, $\\{111,115,92,38,193\\}$,
$\\{9,186,175,161,51\\}$,

$\\{91,152,112,195,158\\}$, $\\{209,121,151,143,148\\}$,
$\\{0,1,143,145,208\\}$,

$\\{0,18,69,141,183\\}$, $\\{0,15,70,117,188\\}$, $\\{0,9,71,96,194\\}$,

$\\{0,7,48,91,108\\}$, $\\{0,20,57,113,181\\}$, $\\{0,12,112,138,184\\}$,

$\\{0,13,49,78,94\\}$, $\\{0,44,88,132,220\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}176)$ for $x<176$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}44))+176$ for $176\leq x<220$, $220\mapsto
220$, $0\leq j<176$ for the first 13 blocks, $0\leq j<44$ for the last block.
[(221, ((13, 176, ((176, 1), (44, 1), (1, 1))), (1, 44, ((176, 1), (44, 1),
(1, 1)))), ((1, 176), (45, 1)))]

$1^{184}21^{1}$ With the point set $\\{0,1,\dots,204\\}$ partitioned into
residue classes modulo $184$ for $\\{0,1,\dots,183\\}$, and
$\\{184,185,\dots,204\\}$, the design is generated from

$\\{36,2,116,109,165\\}$, $\\{24,102,124,125,28\\}$, $\\{68,197,131,0,157\\}$,

$\\{71,52,119,157,88\\}$, $\\{0,3,15,50,199\\}$, $\\{0,13,42,103,200\\}$,

$\\{0,2,18,120,145\\}$, $\\{0,6,20,132,160\\}$, $\\{0,5,37,45,130\\}$,

$\\{0,9,60,71,186\\}$, $\\{0,10,43,119,196\\}$, $\\{0,46,92,138,204\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}184)$ for $x<184$,
$x\mapsto(x-184+2j~{}(\mathrm{mod}~{}16))+184$ for $184\leq x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+200$ for $200\leq x<204$, $204\mapsto
204$, $0\leq j<184$ for the first 11 blocks, $0\leq j<46$ for the last block.
[(205, ((11, 184, ((184, 1), (16, 2), (4, 1), (1, 1))), (1, 46, ((184, 1),
(16, 2), (4, 1), (1, 1)))), ((1, 184), (21, 1)))]

$1^{184}41^{1}$ With the point set $\\{0,1,\dots,224\\}$ partitioned into
residue classes modulo $184$ for $\\{0,1,\dots,183\\}$, and
$\\{184,185,\dots,224\\}$, the design is generated from

$\\{200,80,93,174,155\\}$, $\\{71,185,177,148,14\\}$, $\\{70,96,61,217,58\\}$,

$\\{20,121,208,24,85\\}$, $\\{219,136,1,26,85\\}$, $\\{214,29,115,182,122\\}$,

$\\{0,20,63,131,193\\}$, $\\{0,14,41,140,202\\}$, $\\{0,1,16,96,129\\}$,

$\\{0,10,76,115,206\\}$, $\\{0,6,17,54,156\\}$, $\\{0,2,24,32,144\\}$,

$\\{0,5,52,166,201\\}$, $\\{0,46,92,138,224\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}184)$ for $x<184$,
$x\mapsto(x-184+5j~{}(\mathrm{mod}~{}40))+184$ for $184\leq x<224$,
$224\mapsto 224$, $0\leq j<184$ for the first 13 blocks, $0\leq j<46$ for the
last block.
[(225, ((13, 184, ((184, 1), (40, 5), (1, 1))), (1, 46, ((184, 1), (40, 5),
(1, 1)))), ((1, 184), (41, 1)))]

$1^{188}29^{1}$ With the point set $\\{0,1,\dots,216\\}$ partitioned into
residue classes modulo $188$ for $\\{0,1,\dots,187\\}$, and
$\\{188,189,\dots,216\\}$, the design is generated from

$\\{209,108,5,82,71\\}$, $\\{109,196,182,148,119\\}$,
$\\{124,79,170,110,66\\}$,

$\\{204,56,107,106,125\\}$, $\\{0,2,5,27,191\\}$, $\\{0,6,21,95,194\\}$,

$\\{0,17,59,82,193\\}$, $\\{0,30,79,117,192\\}$, $\\{0,4,24,102,156\\}$,

$\\{0,8,61,70,113\\}$, $\\{0,12,67,108,124\\}$, $\\{0,7,35,107,155\\}$,

$\\{0,47,94,141,216\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}188)$ for $x<188$,
$x\mapsto(x-188+7j~{}(\mathrm{mod}~{}28))+188$ for $188\leq x<216$,
$216\mapsto 216$, $0\leq j<188$ for the first 12 blocks, $0\leq j<47$ for the
last block.
[(217, ((12, 188, ((188, 1), (28, 7), (1, 1))), (1, 47, ((188, 1), (28, 7),
(1, 1)))), ((1, 188), (29, 1)))]

$1^{192}17^{1}$ With the point set $\\{0,1,\dots,208\\}$ partitioned into
residue classes modulo $192$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,208\\}$, the design is generated from

$\\{43,188,94,101,134\\}$, $\\{189,115,101,119,39\\}$,
$\\{116,135,188,166,99\\}$,

$\\{129,88,134,190,202\\}$, $\\{0,1,3,12,129\\}$, $\\{0,28,60,99,137\\}$,

$\\{0,16,43,111,135\\}$, $\\{0,15,52,162,202\\}$, $\\{0,8,21,86,197\\}$,

$\\{0,6,26,85,169\\}$, $\\{0,10,35,158,193\\}$, $\\{0,48,96,144,208\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+192$ for $192\leq x<208$, $208\mapsto
208$, $0\leq j<192$ for the first 11 blocks, $0\leq j<48$ for the last block.
[(209, ((11, 192, ((192, 1), (16, 1), (1, 1))), (1, 48, ((192, 1), (16, 1),
(1, 1)))), ((1, 192), (17, 1)))]

$1^{192}37^{1}$ With the point set $\\{0,1,\dots,228\\}$ partitioned into
residue classes modulo $192$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,228\\}$, the design is generated from

$\\{128,120,2,201,90\\}$, $\\{182,67,222,58,72\\}$, $\\{152,61,7,156,85\\}$,

$\\{41,62,206,168,74\\}$, $\\{72,83,44,128,28\\}$, $\\{219,29,54,2,3\\}$,

$\\{0,35,105,151,218\\}$, $\\{0,15,32,72,90\\}$, $\\{0,2,36,85,200\\}$,

$\\{0,3,22,64,133\\}$, $\\{0,7,80,179,202\\}$, $\\{0,10,63,113,196\\}$,

$\\{0,6,29,161,214\\}$, $\\{0,48,96,144,228\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+192$ for $192\leq x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+216$ for $216\leq x<228$, $228\mapsto
228$, $0\leq j<192$ for the first 13 blocks, $0\leq j<48$ for the last block.
[(229, ((13, 192, ((192, 1), (24, 1), (12, 1), (1, 1))), (1, 48, ((192, 1),
(24, 1), (12, 1), (1, 1)))), ((1, 192), (37, 1)))]

$1^{192}57^{1}$ With the point set $\\{0,1,\dots,248\\}$ partitioned into
residue classes modulo $192$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,248\\}$, the design is generated from

$\\{60,186,233,46,43\\}$, $\\{165,107,65,211,50\\}$,
$\\{93,113,193,120,77\\}$,

$\\{27,237,101,83,182\\}$, $\\{57,238,78,82,90\\}$,
$\\{174,246,61,143,114\\}$,

$\\{80,124,57,200,119\\}$, $\\{0,26,61,146,227\\}$, $\\{0,1,11,76,246\\}$,

$\\{0,6,38,128,147\\}$, $\\{0,9,68,98,199\\}$, $\\{0,40,95,145,202\\}$,

$\\{0,24,78,112,205\\}$, $\\{0,22,63,91,214\\}$, $\\{0,2,73,86,220\\}$,

$\\{0,48,96,144,248\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}32))+192$ for $192\leq x<224$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+224$ for $224\leq x<240$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+240$ for $240\leq x<248$, $248\mapsto
248$, $0\leq j<192$ for the first 15 blocks, $0\leq j<48$ for the last block.
[(249, ((15, 192, ((192, 1), (32, 1), (16, 1), (8, 1), (1, 1))), (1, 48,
((192, 1), (32, 1), (16, 1), (8, 1), (1, 1)))), ((1, 192), (57, 1)))]

$1^{196}25^{1}$ With the point set $\\{0,1,\dots,220\\}$ partitioned into
residue classes modulo $196$ for $\\{0,1,\dots,195\\}$, and
$\\{196,197,\dots,220\\}$, the design is generated from

$\\{53,122,200,96,131\\}$, $\\{147,142,120,179,139\\}$,
$\\{202,25,102,32,183\\}$,

$\\{130,204,147,13,76\\}$, $\\{16,47,144,57,168\\}$, $\\{0,1,83,106,201\\}$,

$\\{0,11,53,146,199\\}$, $\\{0,21,55,94,197\\}$, $\\{0,6,57,72,86\\}$,

$\\{0,12,25,58,132\\}$, $\\{0,2,20,67,168\\}$, $\\{0,4,60,96,112\\}$,

$\\{0,49,98,147,220\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}196)$ for $x<196$,
$x\mapsto(x-196+6j~{}(\mathrm{mod}~{}24))+196$ for $196\leq x<220$,
$220\mapsto 220$, $0\leq j<196$ for the first 12 blocks, $0\leq j<49$ for the
last block.
[(221, ((12, 196, ((196, 1), (24, 6), (1, 1))), (1, 49, ((196, 1), (24, 6),
(1, 1)))), ((1, 196), (25, 1)))]

$1^{196}45^{1}$ With the point set $\\{0,1,\dots,240\\}$ partitioned into
residue classes modulo $196$ for $\\{0,1,\dots,195\\}$, and
$\\{196,197,\dots,240\\}$, the design is generated from

$\\{76,239,147,146,161\\}$, $\\{191,84,112,138,149\\}$,
$\\{7,233,12,174,165\\}$,

$\\{224,124,145,94,151\\}$, $\\{182,230,157,27,60\\}$,
$\\{175,116,85,203,81\\}$,

$\\{161,219,57,12,89\\}$, $\\{0,2,20,82,138\\}$, $\\{0,7,24,68,91\\}$,

$\\{0,3,22,123,203\\}$, $\\{0,8,108,121,221\\}$, $\\{0,16,55,103,210\\}$,

$\\{0,12,64,127,216\\}$, $\\{0,10,46,156,205\\}$, $\\{0,49,98,147,240\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}196)$ for $x<196$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}28))+196$ for $196\leq x<224$,
$x\mapsto(x+4j~{}(\mathrm{mod}~{}16))+224$ for $224\leq x<240$, $240\mapsto
240$, $0\leq j<196$ for the first 14 blocks, $0\leq j<49$ for the last block.
[(241, ((14, 196, ((196, 1), (28, 1), (16, 4), (1, 1))), (1, 49, ((196, 1),
(28, 1), (16, 4), (1, 1)))), ((1, 196), (45, 1)))]

$2^{32}14^{1}$ With the point set $\\{0,1,\dots,77\\}$ partitioned into
residue classes modulo $32$ for $\\{0,1,\dots,63\\}$, and
$\\{64,65,\dots,77\\}$, the design is generated from

$\\{0,11,20,53,65\\}$, $\\{0,1,7,62,76\\}$, $\\{0,4,30,43,69\\}$,

$\\{0,23,59,63,64\\}$, $\\{0,12,49,57,66\\}$, $\\{0,6,16,24,41\\}$,

$\\{0,5,21,31,51\\}$, $\\{0,14,42,61,73\\}$, $\\{0,15,27,29,75\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}64)$ for $x<64$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+64$ for $64\leq x<72$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+72$ for $72\leq x<76$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+76$ for $x\geq 76$, $0\leq j<32$.
[(78, ((9, 32, ((64, 2), (8, 1), (4, 1), (2, 1)))), ((2, 32), (14, 1)))]

$2^{40}6^{1}$ With the point set $\\{0,1,\dots,85\\}$ partitioned into residue
classes modulo $40$ for $\\{0,1,\dots,79\\}$, and $\\{80,81,\dots,85\\}$, the
design is generated from

$\\{51,31,63,50,27\\}$, $\\{4,7,69,34,71\\}$, $\\{0,2,7,73,80\\}$,

$\\{0,6,49,75,82\\}$, $\\{0,20,41,51,79\\}$, $\\{0,11,45,62,81\\}$,

$\\{0,8,17,23,64\\}$, $\\{0,19,27,52,77\\}$, $\\{0,4,14,46,58\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x-80+3j~{}(\mathrm{mod}~{}6))+80$ for $x\geq 80$, $0\leq j<40$.
[(86, ((9, 40, ((80, 2), (6, 3)))), ((2, 40), (6, 1)))]

$2^{48}18^{1}$ With the point set $\\{0,1,\dots,113\\}$ partitioned into
residue classes modulo $48$ for $\\{0,1,\dots,95\\}$, and
$\\{96,97,\dots,113\\}$, the design is generated from

$\\{111,83,60,53,38\\}$, $\\{15,79,50,48,84\\}$, $\\{80,3,98,19,57\\}$,

$\\{0,5,32,58,79\\}$, $\\{0,1,3,9,108\\}$, $\\{0,6,39,82,112\\}$,

$\\{0,8,65,80,93\\}$, $\\{0,41,51,75,87\\}$, $\\{0,7,66,83,101\\}$,

$\\{1,5,57,83,107\\}$, $\\{0,11,12,52,97\\}$, $\\{0,10,59,78,105\\}$,

$\\{0,4,46,71,98\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}96)$ for $x<96$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+96$ for $96\leq x<108$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}6))+108$ for $x\geq 108$, $0\leq j<48$.
[(114, ((13, 48, ((96, 2), (12, 1), (6, 1)))), ((2, 48), (18, 1)))]

$2^{52}14^{1}$ With the point set $\\{0,1,\dots,117\\}$ partitioned into
residue classes modulo $52$ for $\\{0,1,\dots,103\\}$, and
$\\{104,105,\dots,117\\}$, the design is generated from

$\\{55,54,97,0,15\\}$, $\\{26,87,56,109,29\\}$, $\\{112,30,83,65,20\\}$,

$\\{16,83,11,27,95\\}$, $\\{0,2,9,103,108\\}$, $\\{0,5,39,86,104\\}$,

$\\{0,13,17,46,93\\}$, $\\{0,25,51,70,106\\}$, $\\{0,21,81,87,95\\}$,

$\\{0,27,29,42,107\\}$, $\\{0,14,33,83,110\\}$, $\\{0,4,41,72,96\\}$,

$\\{0,6,26,66,82\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}104)$ for $x<104$,
$x\mapsto(x-104+7j~{}(\mathrm{mod}~{}14))+104$ for $x\geq 104$, $0\leq j<52$.
[(118, ((13, 52, ((104, 2), (14, 7)))), ((2, 52), (14, 1)))]

$2^{56}10^{1}$ With the point set $\\{0,1,\dots,121\\}$ partitioned into
residue classes modulo $56$ for $\\{0,1,\dots,111\\}$, and
$\\{112,113,\dots,121\\}$, the design is generated from

$\\{120,105,88,79,102\\}$, $\\{20,107,10,52,16\\}$, $\\{20,78,116,105,45\\}$,

$\\{67,72,116,26,31\\}$, $\\{0,1,2,92,116\\}$, $\\{0,15,37,49,113\\}$,

$\\{0,8,26,61,77\\}$, $\\{0,9,29,48,82\\}$, $\\{0,7,44,72,96\\}$,

$\\{0,12,43,45,74\\}$, $\\{0,13,19,63,101\\}$, $\\{0,11,57,65,105\\}$,

$\\{0,67,95,99,109\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}112)$ for $x<112$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+112$ for $112\leq x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+120$ for $x\geq 120$, $0\leq j<56$.
[(122, ((13, 56, ((112, 2), (8, 1), (2, 1)))), ((2, 56), (10, 1)))]

$2^{60}6^{1}$ With the point set $\\{0,1,\dots,125\\}$ partitioned into
residue classes modulo $60$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,125\\}$, the design is generated from

$\\{15,81,4,83,10\\}$, $\\{39,123,56,22,109\\}$, $\\{80,73,102,77,8\\}$,

$\\{20,102,124,98,105\\}$, $\\{62,54,52,34,43\\}$, $\\{0,15,55,93,122\\}$,

$\\{0,12,36,63,68\\}$, $\\{0,14,30,59,80\\}$, $\\{0,1,21,37,74\\}$,

$\\{0,25,33,39,57\\}$, $\\{0,23,49,62,97\\}$, $\\{0,19,31,41,75\\}$,

$\\{0,13,43,44,105\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}6))+120$ for $x\geq 120$, $0\leq j<60$.
[(126, ((13, 60, ((120, 2), (6, 1)))), ((2, 60), (6, 1)))]

$3^{20}11^{1}$ With the point set $\\{0,1,\dots,70\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,59\\}$, and
$\\{60,61,\dots,70\\}$, the design is generated from

$\\{0,3,11,38,61\\}$, $\\{0,1,5,7,44\\}$, $\\{0,13,29,55,69\\}$,

$\\{0,2,10,37,51\\}$, $\\{0,9,31,59,63\\}$, $\\{0,4,43,46,68\\}$,

$\\{0,6,34,53,67\\}$, $\\{0,15,30,45,70\\}$, $\\{0,12,24,36,48\\}$,

$\\{1,13,25,37,49\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}60)$ for $x<60$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}10))+60$ for $60\leq x<70$, $70\mapsto 70$,
$0\leq j<30$ for the first seven blocks, $0\leq j<15$ for the next block,
$0\leq j<6$ for the last two blocks.
[(71, ((7, 30, ((60, 2), (10, 1), (1, 1))), (1, 15, ((60, 2), (10, 1), (1,
1))), (2, 6, ((60, 2), (10, 1), (1, 1)))), ((3, 20), (11, 1)))]

$3^{28}7^{1}$ With the point set $\\{0,1,\dots,90\\}$ partitioned into residue
classes modulo $28$ for $\\{0,1,\dots,83\\}$, and $\\{84,85,\dots,90\\}$, the
design is generated from

$\\{0,60,9,82,50\\}$, $\\{9,15,19,49,58\\}$, $\\{0,1,8,59,78\\}$,

$\\{0,19,57,71,79\\}$, $\\{0,16,53,55,90\\}$, $\\{0,3,38,64,69\\}$,

$\\{0,12,27,30,86\\}$, $\\{0,47,67,83,88\\}$, $\\{0,4,17,29,40\\}$,

$\\{0,21,42,63,84\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}84)$ for $x<84$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}7))+84$ for $x\geq 84$, $0\leq j<42$ for the
first nine blocks, $0\leq j<21$ for the last block.
[(91, ((9, 42, ((84, 2), (7, 1))), (1, 21, ((84, 2), (7, 1)))), ((3, 28), (7,
1)))]

$3^{32}11^{1}$ With the point set $\\{0,1,\dots,106\\}$ partitioned into
residue classes modulo $32$ for $\\{0,1,\dots,95\\}$, and
$\\{96,97,\dots,106\\}$, the design is generated from

$\\{99,75,72,57,14\\}$, $\\{8,101,2,55,21\\}$, $\\{23,86,91,0,35\\}$,

$\\{0,1,2,27,98\\}$, $\\{0,14,31,77,97\\}$, $\\{0,18,87,89,100\\}$,

$\\{0,37,41,57,79\\}$, $\\{0,7,59,67,73\\}$, $\\{0,4,15,26,60\\}$,

$\\{0,8,20,29,50\\}$, $\\{0,16,55,65,68\\}$, $\\{0,24,48,72,106\\}$,

$\\{1,25,49,73,106\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}96)$ for $x<96$,
$x\mapsto(x-96+5j~{}(\mathrm{mod}~{}10))+96$ for $96\leq x<106$, $106\mapsto
106$, $0\leq j<48$ for the first 11 blocks, $0\leq j<12$ for the last two
blocks.
[(107, ((11, 48, ((96, 2), (10, 5), (1, 1))), (2, 12, ((96, 2), (10, 5), (1,
1)))), ((3, 32), (11, 1)))]

$3^{36}15^{1}$ With the point set $\\{0,1,\dots,122\\}$ partitioned into
residue classes modulo $36$ for $\\{0,1,\dots,107\\}$, and
$\\{108,109,\dots,122\\}$, the design is generated from

$\\{104,7,20,0,75\\}$, $\\{13,24,37,14,7\\}$, $\\{100,78,116,32,81\\}$,

$\\{54,42,70,107,85\\}$, $\\{0,1,6,39,120\\}$, $\\{0,8,38,56,85\\}$,

$\\{0,14,59,87,111\\}$, $\\{0,2,63,66,119\\}$, $\\{0,5,21,25,115\\}$,

$\\{0,9,57,71,83\\}$, $\\{0,26,67,76,118\\}$, $\\{0,17,35,74,93\\}$,

$\\{1,3,11,67,116\\}$, $\\{0,27,54,81,122\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}108)$ for $x<108$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}12))+108$ for $108\leq x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+120$ for $120\leq x<122$, $122\mapsto
122$, $0\leq j<54$ for the first 13 blocks, $0\leq j<27$ for the last block.
[(123, ((13, 54, ((108, 2), (12, 2), (2, 1), (1, 1))), (1, 27, ((108, 2), (12,
2), (2, 1), (1, 1)))), ((3, 36), (15, 1)))]

$5^{24}25^{1}$ With the point set $\\{0,1,\dots,144\\}$ partitioned into
residue classes modulo $24$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,144\\}$, the design is generated from

$\\{2,54,94,116,13\\}$, $\\{78,105,69,112,134\\}$, $\\{109,31,121,5,96\\}$,

$\\{0,8,61,71,123\\}$, $\\{0,2,21,85,97\\}$, $\\{0,5,20,38,131\\}$,

$\\{0,1,32,46,120\\}$, $\\{0,3,69,73,130\\}$, $\\{0,30,60,90,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+120$ for $120\leq x<144$, $144\mapsto
144$, $0\leq j<120$ for the first eight blocks, $0\leq j<30$ for the last
block.
[(145, ((8, 120, ((120, 1), (24, 1), (1, 1))), (1, 30, ((120, 1), (24, 1), (1,
1)))), ((5, 24), (25, 1)))]

$5^{28}25^{1}$ With the point set $\\{0,1,\dots,164\\}$ partitioned into
residue classes modulo $28$ for $\\{0,1,\dots,139\\}$, and
$\\{140,141,\dots,164\\}$, the design is generated from

$\\{41,28,158,75,14\\}$, $\\{107,154,33,108,65\\}$, $\\{50,0,145,137,46\\}$,

$\\{0,2,17,39,160\\}$, $\\{0,12,38,83,154\\}$, $\\{0,6,25,58,158\\}$,

$\\{0,5,16,36,116\\}$, $\\{0,7,30,51,92\\}$, $\\{0,8,18,72,81\\}$,

$\\{0,35,70,105,164\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}140)$ for $x<140$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+140$ for $140\leq x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+160$ for $160\leq x<164$, $164\mapsto
164$, $0\leq j<140$ for the first nine blocks, $0\leq j<35$ for the last
block.
[(165, ((9, 140, ((140, 1), (20, 1), (4, 1), (1, 1))), (1, 35, ((140, 1), (20,
1), (4, 1), (1, 1)))), ((5, 28), (25, 1)))]

$5^{32}25^{1}$ With the point set $\\{0,1,\dots,184\\}$ partitioned into
residue classes modulo $32$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,184\\}$, the design is generated from

$\\{35,27,136,171,2\\}$, $\\{75,90,104,22,176\\}$, $\\{69,129,50,123,107\\}$,

$\\{0,1,3,10,180\\}$, $\\{0,11,31,86,130\\}$, $\\{0,12,36,83,133\\}$,

$\\{0,21,58,93,171\\}$, $\\{0,28,70,104,167\\}$, $\\{0,5,23,117,165\\}$,

$\\{0,4,17,69,115\\}$, $\\{0,40,80,120,184\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+160$ for $160\leq x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+180$ for $180\leq x<184$, $184\mapsto
184$, $0\leq j<160$ for the first ten blocks, $0\leq j<40$ for the last block.
[(185, ((10, 160, ((160, 1), (20, 1), (4, 1), (1, 1))), (1, 40, ((160, 1),
(20, 1), (4, 1), (1, 1)))), ((5, 32), (25, 1)))]

$5^{32}45^{1}$ With the point set $\\{0,1,\dots,204\\}$ partitioned into
residue classes modulo $32$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,204\\}$, the design is generated from

$\\{169,28,2,16,88\\}$, $\\{186,137,94,89,124\\}$, $\\{139,173,28,56,80\\}$,

$\\{95,170,32,26,116\\}$, $\\{0,1,3,10,200\\}$, $\\{0,4,15,109,180\\}$,

$\\{0,8,46,62,93\\}$, $\\{0,18,41,133,188\\}$, $\\{0,19,53,135,171\\}$,

$\\{0,17,56,127,166\\}$, $\\{0,20,81,123,163\\}$, $\\{0,22,58,87,186\\}$,

$\\{0,40,80,120,204\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}40))+160$ for $160\leq x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+200$ for $200\leq x<204$, $204\mapsto
204$, $0\leq j<160$ for the first 12 blocks, $0\leq j<40$ for the last block.
[(205, ((12, 160, ((160, 1), (40, 1), (4, 1), (1, 1))), (1, 40, ((160, 1),
(40, 1), (4, 1), (1, 1)))), ((5, 32), (45, 1)))]

$5^{36}45^{1}$ With the point set $\\{0,1,\dots,224\\}$ partitioned into
residue classes modulo $36$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,224\\}$, the design is generated from

$\\{99,71,104,57,34\\}$, $\\{9,73,88,219,164\\}$, $\\{99,130,190,16,67\\}$,

$\\{75,86,214,8,92\\}$, $\\{96,109,2,28,185\\}$, $\\{0,1,4,160,162\\}$,

$\\{0,35,93,141,223\\}$, $\\{0,10,59,134,203\\}$, $\\{0,8,60,100,207\\}$,

$\\{0,30,71,125,186\\}$, $\\{0,9,38,136,209\\}$, $\\{0,16,43,77,185\\}$,

$\\{0,7,118,130,222\\}$, $\\{0,45,90,135,180\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}45))+180$ for $x\geq 180$, $0\leq j<180$ for
the first 13 blocks, $0\leq j<45$ for the last block.
[(225, ((13, 180, ((180, 1), (45, 1))), (1, 45, ((180, 1), (45, 1)))), ((5,
36), (45, 1)))]

$5^{40}45^{1}$ With the point set $\\{0,1,\dots,244\\}$ partitioned into
residue classes modulo $40$ for $\\{0,1,\dots,199\\}$, and
$\\{200,201,\dots,244\\}$, the design is generated from

$\\{100,67,95,19,199\\}$, $\\{230,112,88,70,186\\}$, $\\{98,88,61,104,210\\}$,

$\\{243,153,6,75,36\\}$, $\\{75,0,94,12,23\\}$, $\\{213,125,34,36,94\\}$,

$\\{0,4,17,107,205\\}$, $\\{0,1,46,55,231\\}$, $\\{0,15,47,88,221\\}$,

$\\{0,8,34,70,95\\}$, $\\{0,3,38,67,210\\}$, $\\{0,7,92,151,227\\}$,

$\\{0,14,65,86,209\\}$, $\\{0,22,79,156,233\\}$, $\\{0,50,100,150,244\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}200)$ for $x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}40))+200$ for $200\leq x<240$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+240$ for $240\leq x<244$, $244\mapsto
244$, $0\leq j<200$ for the first 14 blocks, $0\leq j<50$ for the last block.
[(245, ((14, 200, ((200, 1), (40, 1), (4, 1), (1, 1))), (1, 50, ((200, 1),
(40, 1), (4, 1), (1, 1)))), ((5, 40), (45, 1)))]

$5^{44}25^{1}$ With the point set $\\{0,1,\dots,244\\}$ partitioned into
residue classes modulo $44$ for $\\{0,1,\dots,219\\}$, and
$\\{220,221,\dots,244\\}$, the design is generated from

$\\{48,152,234,101,49\\}$, $\\{20,181,213,144,38\\}$,
$\\{216,27,93,118,135\\}$,

$\\{14,148,158,184,156\\}$, $\\{142,119,231,176,17\\}$, $\\{0,3,9,14,240\\}$,

$\\{0,22,62,127,162\\}$, $\\{0,13,33,54,146\\}$, $\\{0,4,16,64,153\\}$,

$\\{0,15,99,145,223\\}$, $\\{0,7,63,101,148\\}$, $\\{0,29,68,138,239\\}$,

$\\{0,19,49,196,236\\}$, $\\{0,55,110,165,244\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}220)$ for $x<220$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+220$ for $220\leq x<240$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+240$ for $240\leq x<244$, $244\mapsto
244$, $0\leq j<220$ for the first 13 blocks, $0\leq j<55$ for the last block.
[(245, ((13, 220, ((220, 1), (20, 1), (4, 1), (1, 1))), (1, 55, ((220, 1),
(20, 1), (4, 1), (1, 1)))), ((5, 44), (25, 1)))]

$5^{44}45^{1}$ With the point set $\\{0,1,\dots,264\\}$ partitioned into
residue classes modulo $44$ for $\\{0,1,\dots,219\\}$, and
$\\{220,221,\dots,264\\}$, the design is generated from

$\\{238,107,38,100,124\\}$, $\\{144,135,226,109,104\\}$,
$\\{54,151,223,214,102\\}$,

$\\{4,72,260,33,1\\}$, $\\{64,164,250,202,148\\}$, $\\{258,218,11,21,135\\}$,

$\\{230,134,123,53,33\\}$, $\\{0,12,65,117,145\\}$, $\\{0,8,164,178,233\\}$,

$\\{0,30,89,146,252\\}$, $\\{0,15,37,73,235\\}$, $\\{0,4,111,129,240\\}$,

$\\{0,33,67,118,159\\}$, $\\{0,1,77,79,122\\}$, $\\{0,6,25,72,199\\}$,

$\\{0,55,110,165,264\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}220)$ for $x<220$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}44))+220$ for $220\leq x<264$, $264\mapsto
264$, $0\leq j<220$ for the first 15 blocks, $0\leq j<55$ for the last block.
[(265, ((15, 220, ((220, 1), (44, 1), (1, 1))), (1, 55, ((220, 1), (44, 1),
(1, 1)))), ((5, 44), (45, 1)))]

$6^{16}10^{1}$ With the point set $\\{0,1,\dots,105\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,95\\}$, and
$\\{96,97,\dots,105\\}$, the design is generated from

$\\{105,17,83,38,28\\}$, $\\{20,99,63,48,94\\}$, $\\{95,58,60,11,84\\}$,

$\\{0,1,4,7,40\\}$, $\\{0,9,18,52,103\\}$, $\\{0,29,31,51,58\\}$,

$\\{0,12,66,83,91\\}$, $\\{0,5,6,33,88\\}$, $\\{0,19,61,76,96\\}$,

$\\{1,11,35,61,102\\}$, $\\{0,21,59,73,77\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}96)$ for $x<96$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+96$ for $96\leq x<104$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+104$ for $x\geq 104$, $0\leq j<48$.
[(106, ((11, 48, ((96, 2), (8, 1), (2, 1)))), ((6, 16), (10, 1)))]

$8^{8}12^{1}$ With the point set $\\{0,1,\dots,75\\}$ partitioned into residue
classes modulo $8$ for $\\{0,1,\dots,63\\}$, and $\\{64,65,\dots,75\\}$, the
design is generated from

$\\{49,48,72,18,31\\}$, $\\{55,48,50,12,69\\}$, $\\{20,26,29,40,68\\}$,

$\\{0,4,19,29,41\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}64)$ for $x<64$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+64$ for $64\leq x<72$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+72$ for $x\geq 72$, $0\leq j<64$.
[(76, ((4, 64, ((64, 1), (8, 1), (4, 1)))), ((8, 8), (12, 1)))]

$8^{10}16^{1}$ With the point set $\\{0,1,\dots,95\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,79\\}$, and
$\\{80,81,\dots,95\\}$, the design is generated from

$\\{0,1,4,6,23\\}$, $\\{0,8,42,51,90\\}$, $\\{0,11,26,44,89\\}$,

$\\{0,7,21,56,91\\}$, $\\{0,12,25,53,81\\}$, $\\{0,16,32,48,64\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+80$ for $x\geq 80$, $0\leq j<80$ for the
first five blocks, $0\leq j<16$ for the last block.
[(96, ((5, 80, ((80, 1), (16, 1))), (1, 16, ((80, 1), (16, 1)))), ((8, 10),
(16, 1)))]

$8^{10}20^{1}$ With the point set $\\{0,1,\dots,99\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,79\\}$, and
$\\{80,81,\dots,99\\}$, the design is generated from

$\\{90,78,79,50,76\\}$, $\\{86,50,6,55,17\\}$, $\\{63,46,11,40,29\\}$,

$\\{0,4,12,79,96\\}$, $\\{0,7,14,33,84\\}$, $\\{0,18,56,77,88\\}$,

$\\{0,9,25,34,86\\}$, $\\{0,22,53,65,98\\}$, $\\{0,15,37,39,82\\}$,

$\\{0,13,57,61,95\\}$, $\\{0,27,35,41,93\\}$, $\\{0,16,32,48,64\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}80)$ for $x<80$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+80$ for $x\geq 80$, $0\leq j<40$ for the
first 11 blocks, $0\leq j<8$ for the last block.
[(100, ((11, 40, ((80, 2), (20, 1))), (1, 8, ((80, 2), (20, 1)))), ((8, 10),
(20, 1)))]

$8^{14}28^{1}$ With the point set $\\{0,1,\dots,139\\}$ partitioned into
residue classes modulo $14$ for $\\{0,1,\dots,111\\}$, and
$\\{112,113,\dots,139\\}$, the design is generated from

$\\{127,27,96,108,35\\}$, $\\{1,112,16,26,102\\}$, $\\{0,1,94,110,119\\}$,

$\\{0,4,68,75,116\\}$, $\\{0,13,45,91,130\\}$, $\\{0,9,38,58,136\\}$,

$\\{0,6,30,53,135\\}$, $\\{0,5,27,60,77\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}112)$ for $x<112$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}28))+112$ for $x\geq 112$, $0\leq j<112$.
[(140, ((8, 112, ((112, 1), (28, 1)))), ((8, 14), (28, 1)))]

$8^{15}4^{1}$ With the point set $\\{0,1,\dots,123\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,122,123\\}$, the design is generated from

$\\{101,53,15,51,9\\}$, $\\{23,1,112,2,120\\}$, $\\{0,4,43,61,68\\}$,

$\\{0,3,17,29,100\\}$, $\\{0,8,41,54,73\\}$, $\\{0,5,16,40,67\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+120$ for $x\geq 120$, $0\leq j<120$.
[(124, ((6, 120, ((120, 1), (4, 1)))), ((8, 15), (4, 1)))]

$8^{15}16^{1}$ With the point set $\\{0,1,\dots,135\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,135\\}$, the design is generated from

$\\{0,1,4,6,110\\}$, $\\{0,7,39,47,56\\}$, $\\{0,12,62,89,122\\}$,

$\\{0,18,53,86,128\\}$, $\\{0,26,55,92,121\\}$, $\\{0,13,36,57,82\\}$,

$\\{0,19,78,98,131\\}$, $\\{0,24,48,72,96\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x-120+2j~{}(\mathrm{mod}~{}16))+120$ for $x\geq 120$, $0\leq j<120$
for the first seven blocks; $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x-120+4j~{}(\mathrm{mod}~{}16))+120$ for $x\geq 120$, $0\leq j<24$
for the last block.
[(136, ((7, 120, ((120, 1), (16, 2))), (1, 24, ((120, 1), (16, 4)))), ((8,
15), (16, 1)))]

$8^{15}24^{1}$ With the point set $\\{0,1,\dots,143\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,143\\}$, the design is generated from

$\\{136,16,113,110,36\\}$, $\\{67,140,31,99,14\\}$, $\\{0,1,6,10,102\\}$,

$\\{0,8,22,70,91\\}$, $\\{0,12,59,93,128\\}$, $\\{0,16,57,82,139\\}$,

$\\{0,7,40,71,134\\}$, $\\{0,2,13,78,138\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+120$ for $x\geq 120$, $0\leq j<120$.
[(144, ((8, 120, ((120, 1), (24, 1)))), ((8, 15), (24, 1)))]

$8^{15}36^{1}$ With the point set $\\{0,1,\dots,155\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,155\\}$, the design is generated from

$\\{80,58,155,119,54\\}$, $\\{74,24,129,66,101\\}$, $\\{0,1,3,114,154\\}$,

$\\{0,14,33,54,152\\}$, $\\{0,5,36,88,125\\}$, $\\{0,11,62,82,128\\}$,

$\\{0,10,63,86,136\\}$, $\\{0,17,46,64,132\\}$, $\\{0,12,25,104,131\\}$,

$\\{0,24,48,72,96\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+120$ for $120\leq x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+144$ for $x\geq 144$, $0\leq j<120$ for
the first nine blocks, $0\leq j<24$ for the last block.
[(156, ((9, 120, ((120, 1), (24, 1), (12, 1))), (1, 24, ((120, 1), (24, 1),
(12, 1)))), ((8, 15), (36, 1)))]

$8^{16}20^{1}$ With the point set $\\{0,1,\dots,147\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,127\\}$, and
$\\{128,129,\dots,147\\}$, the design is generated from

$\\{21,31,76,89,27\\}$, $\\{21,74,105,139,54\\}$, $\\{0,1,3,110,144\\}$,

$\\{0,8,71,101,131\\}$, $\\{0,9,34,90,137\\}$, $\\{0,5,17,59,105\\}$,

$\\{0,11,26,50,87\\}$, $\\{0,7,92,106,132\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}128)$ for $x<128$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+128$ for $128\leq x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+144$ for $x\geq 144$, $0\leq j<128$.
[(148, ((8, 128, ((128, 1), (16, 1), (4, 1)))), ((8, 16), (20, 1)))]

$8^{17}16^{1}$ With the point set $\\{0,1,\dots,151\\}$ partitioned into
residue classes modulo $17$ for $\\{0,1,\dots,135\\}$, and
$\\{136,137,\dots,151\\}$, the design is generated from

$\\{82,29,94,18,126\\}$, $\\{60,24,102,87,40\\}$, $\\{0,2,5,24,45\\}$,

$\\{0,8,38,56,69\\}$, $\\{0,7,57,66,140\\}$, $\\{0,1,26,55,148\\}$,

$\\{0,4,103,126,137\\}$, $\\{0,6,52,101,143\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}136)$ for $x<136$,
$x\mapsto(x-136+2j~{}(\mathrm{mod}~{}16))+136$ for $x\geq 136$, $0\leq j<136$.
[(152, ((8, 136, ((136, 1), (16, 2)))), ((8, 17), (16, 1)))]

$8^{18}32^{1}$ With the point set $\\{0,1,\dots,175\\}$ partitioned into
residue classes modulo $18$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,175\\}$, the design is generated from

$\\{60,54,100,156,135\\}$, $\\{162,11,60,77,3\\}$, $\\{45,116,139,25,155\\}$,

$\\{0,1,3,27,152\\}$, $\\{0,13,51,113,160\\}$, $\\{0,10,32,96,111\\}$,

$\\{0,9,21,37,76\\}$, $\\{0,4,29,88,167\\}$, $\\{0,5,19,102,155\\}$,

$\\{0,7,41,52,171\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x-144+2j~{}(\mathrm{mod}~{}32))+144$ for $x\geq 144$, $0\leq j<144$.
[(176, ((10, 144, ((144, 1), (32, 2)))), ((8, 18), (32, 1)))]

$8^{20}44^{1}$ With the point set $\\{0,1,\dots,203\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,203\\}$, the design is generated from

$\\{98,87,68,183,84\\}$, $\\{59,81,116,162,15\\}$, $\\{22,86,53,159,77\\}$,

$\\{174,126,134,152,73\\}$, $\\{43,201,85,0,154\\}$, $\\{0,1,29,113,164\\}$,

$\\{0,2,67,88,180\\}$, $\\{0,25,62,133,170\\}$, $\\{0,4,50,147,177\\}$,

$\\{0,12,70,104,186\\}$, $\\{0,5,41,150,199\\}$, $\\{0,7,39,122,191\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}40))+160$ for $160\leq x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+200$ for $x\geq 200$, $0\leq j<160$.
[(204, ((12, 160, ((160, 1), (40, 1), (4, 1)))), ((8, 20), (44, 1)))]

$8^{21}20^{1}$ With the point set $\\{0,1,\dots,187\\}$ partitioned into
residue classes modulo $21$ for $\\{0,1,\dots,167\\}$, and
$\\{168,169,\dots,187\\}$, the design is generated from

$\\{127,171,77,36,42\\}$, $\\{145,58,180,136,11\\}$, $\\{48,0,33,29,103\\}$,

$\\{0,1,3,146,172\\}$, $\\{0,5,18,67,175\\}$, $\\{0,7,38,89,184\\}$,

$\\{0,11,27,122,142\\}$, $\\{0,12,64,92,109\\}$, $\\{0,10,40,54,112\\}$,

$\\{0,8,32,68,107\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}168)$ for $x<168$,
$x\mapsto(x-168+2j~{}(\mathrm{mod}~{}16))+168$ for $168\leq x<184$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+184$ for $x\geq 184$, $0\leq j<168$.
[(188, ((10, 168, ((168, 1), (16, 2), (4, 1)))), ((8, 21), (20, 1)))]

$8^{21}40^{1}$ With the point set $\\{0,1,\dots,207\\}$ partitioned into
residue classes modulo $21$ for $\\{0,1,\dots,167\\}$, and
$\\{168,169,\dots,207\\}$, the design is generated from

$\\{178,42,76,70,122\\}$, $\\{116,191,138,85,21\\}$, $\\{88,174,58,47,45\\}$,

$\\{142,189,125,109,55\\}$, $\\{0,1,103,165,192\\}$, $\\{0,7,57,86,204\\}$,

$\\{0,12,48,72,109\\}$, $\\{0,8,27,47,85\\}$, $\\{0,10,25,100,181\\}$,

$\\{0,18,67,112,175\\}$, $\\{0,23,92,136,194\\}$, $\\{0,5,14,40,191\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}168)$ for $x<168$,
$x\mapsto(x-168+3j~{}(\mathrm{mod}~{}36))+168$ for $168\leq x<204$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+204$ for $x\geq 204$, $0\leq j<168$.
[(208, ((12, 168, ((168, 1), (36, 3), (4, 1)))), ((8, 21), (40, 1)))]

$8^{22}16^{1}$ With the point set $\\{0,1,\dots,191\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,175\\}$, and
$\\{176,177,\dots,191\\}$, the design is generated from

$\\{191,130,134,128,107\\}$, $\\{62,112,77,15,44\\}$,
$\\{152,57,89,37,106\\}$,

$\\{0,1,8,11,104\\}$, $\\{0,5,36,75,123\\}$, $\\{0,16,57,76,121\\}$,

$\\{0,14,42,98,136\\}$, $\\{0,13,37,146,179\\}$, $\\{0,25,59,150,176\\}$,

$\\{0,9,99,111,187\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}176)$ for $x<176$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+176$ for $x\geq 176$, $0\leq j<176$.
[(192, ((10, 176, ((176, 1), (16, 1)))), ((8, 22), (16, 1)))]

$8^{22}36^{1}$ With the point set $\\{0,1,\dots,211\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,175\\}$, and
$\\{176,177,\dots,211\\}$, the design is generated from

$\\{40,88,91,38,130\\}$, $\\{114,49,105,31,205\\}$,
$\\{101,198,162,127,115\\}$,

$\\{58,13,205,68,30\\}$, $\\{0,1,6,31,208\\}$, $\\{0,4,15,122,181\\}$,

$\\{0,29,75,127,189\\}$, $\\{0,8,32,99,112\\}$, $\\{0,23,105,139,204\\}$,

$\\{0,16,36,57,133\\}$, $\\{0,7,40,113,180\\}$, $\\{0,19,81,108,176\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}176)$ for $x<176$,
$x\mapsto(x-176+2j~{}(\mathrm{mod}~{}32))+176$ for $176\leq x<208$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+208$ for $x\geq 208$, $0\leq j<176$.
[(212, ((12, 176, ((176, 1), (32, 2), (4, 1)))), ((8, 22), (36, 1)))]

$8^{23}32^{1}$ With the point set $\\{0,1,\dots,215\\}$ partitioned into
residue classes modulo $23$ for $\\{0,1,\dots,183\\}$, and
$\\{184,185,\dots,215\\}$, the design is generated from

$\\{120,119,172,2,29\\}$, $\\{186,180,73,182,101\\}$, $\\{24,20,209,54,98\\}$,

$\\{205,142,18,152,116\\}$, $\\{0,3,20,25,190\\}$, $\\{0,7,15,39,102\\}$,

$\\{0,13,29,112,149\\}$, $\\{0,9,49,80,137\\}$, $\\{0,21,76,146,204\\}$,

$\\{0,6,139,172,192\\}$, $\\{0,19,61,119,187\\}$, $\\{0,11,73,141,215\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}184)$ for $x<184$,
$x\mapsto(x-184+4j~{}(\mathrm{mod}~{}32))+184$ for $x\geq 184$, $0\leq j<184$.
[(216, ((12, 184, ((184, 1), (32, 4)))), ((8, 23), (32, 1)))]

$8^{24}28^{1}$ With the point set $\\{0,1,\dots,219\\}$ partitioned into
residue classes modulo $24$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,219\\}$, the design is generated from

$\\{187,133,147,68,180\\}$, $\\{56,62,106,44,87\\}$,
$\\{119,111,25,91,182\\}$,

$\\{186,3,118,134,206\\}$, $\\{71,75,174,92,175\\}$, $\\{0,2,15,57,216\\}$,

$\\{0,29,74,143,198\\}$, $\\{0,5,107,158,200\\}$, $\\{0,32,70,116,205\\}$,

$\\{0,3,26,56,67\\}$, $\\{0,22,58,133,204\\}$, $\\{0,10,105,165,211\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+192$ for $192\leq x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+216$ for $x\geq 216$, $0\leq j<192$.
[(220, ((12, 192, ((192, 1), (24, 1), (4, 1)))), ((8, 24), (28, 1)))]

$8^{25}4^{1}$ With the point set $\\{0,1,\dots,203\\}$ partitioned into
residue classes modulo $25$ for $\\{0,1,\dots,199\\}$, and
$\\{200,201,202,203\\}$, the design is generated from

$\\{61,123,191,58,177\\}$, $\\{126,154,132,152,9\\}$,
$\\{127,42,131,95,173\\}$,

$\\{0,1,30,35,200\\}$, $\\{0,9,27,91,107\\}$, $\\{0,13,58,79,153\\}$,

$\\{0,8,19,52,160\\}$, $\\{0,15,38,101,144\\}$, $\\{0,7,17,104,176\\}$,

$\\{0,12,49,88,139\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}200)$ for $x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+200$ for $x\geq 200$, $0\leq j<200$.
[(204, ((10, 200, ((200, 1), (4, 1)))), ((8, 25), (4, 1)))]

$8^{25}24^{1}$ With the point set $\\{0,1,\dots,223\\}$ partitioned into
residue classes modulo $25$ for $\\{0,1,\dots,199\\}$, and
$\\{200,201,\dots,223\\}$, the design is generated from

$\\{67,86,68,183,121\\}$, $\\{178,59,217,68,12\\}$, $\\{168,154,37,26,63\\}$,

$\\{77,163,14,183,50\\}$, $\\{159,205,181,24,183\\}$, $\\{0,3,10,161,220\\}$,

$\\{0,5,21,129,141\\}$, $\\{0,6,46,79,107\\}$, $\\{0,8,23,52,112\\}$,

$\\{0,4,74,122,217\\}$, $\\{0,13,30,68,200\\}$, $\\{0,32,77,134,208\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}200)$ for $x<200$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+200$ for $200\leq x<220$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+220$ for $x\geq 220$, $0\leq j<200$.
[(224, ((12, 200, ((200, 1), (20, 1), (4, 1)))), ((8, 25), (24, 1)))]

$8^{26}20^{1}$ With the point set $\\{0,1,\dots,227\\}$ partitioned into
residue classes modulo $26$ for $\\{0,1,\dots,207\\}$, and
$\\{208,209,\dots,227\\}$, the design is generated from

$\\{216,58,130,112,1\\}$, $\\{222,17,139,34,5\\}$, $\\{164,68,27,115,70\\}$,

$\\{201,173,31,176,195\\}$, $\\{55,203,199,78,71\\}$, $\\{0,9,30,115,224\\}$,

$\\{0,5,51,82,152\\}$, $\\{0,1,40,195,210\\}$, $\\{0,10,65,181,213\\}$,

$\\{0,8,67,99,135\\}$, $\\{0,11,35,69,119\\}$, $\\{0,15,48,90,110\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}208)$ for $x<208$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+208$ for $208\leq x<224$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+224$ for $x\geq 224$, $0\leq j<208$.
[(228, ((12, 208, ((208, 1), (16, 1), (4, 1)))), ((8, 26), (20, 1)))]

$8^{27}16^{1}$ With the point set $\\{0,1,\dots,231\\}$ partitioned into
residue classes modulo $27$ for $\\{0,1,\dots,215\\}$, and
$\\{216,217,\dots,231\\}$, the design is generated from

$\\{133,29,73,120,195\\}$, $\\{49,198,23,126,6\\}$, $\\{127,75,109,38,43\\}$,

$\\{206,212,198,177,70\\}$, $\\{136,26,187,111,220\\}$,
$\\{0,1,39,138,228\\}$,

$\\{0,2,48,59,63\\}$, $\\{0,16,36,118,183\\}$, $\\{0,12,40,70,123\\}$,

$\\{0,3,119,209,226\\}$, $\\{0,19,42,87,143\\}$, $\\{0,9,31,95,219\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}216)$ for $x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+216$ for $216\leq x<228$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+228$ for $x\geq 228$, $0\leq j<216$.
[(232, ((12, 216, ((216, 1), (12, 1), (4, 1)))), ((8, 27), (16, 1)))]

$8^{28}12^{1}$ With the point set $\\{0,1,\dots,235\\}$ partitioned into
residue classes modulo $28$ for $\\{0,1,\dots,223\\}$, and
$\\{224,225,\dots,235\\}$, the design is generated from

$\\{136,105,86,206,54\\}$, $\\{235,68,221,2,115\\}$,
$\\{228,146,220,144,143\\}$,

$\\{48,75,36,207,153\\}$, $\\{200,86,222,11,5\\}$, $\\{0,4,126,137,231\\}$,

$\\{0,10,48,103,144\\}$, $\\{0,18,42,86,181\\}$, $\\{0,8,33,67,97\\}$,

$\\{0,15,52,73,109\\}$, $\\{0,16,79,124,141\\}$, $\\{0,9,23,49,69\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}224)$ for $x<224$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+224$ for $224\leq x<232$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+232$ for $x\geq 232$, $0\leq j<224$.
[(236, ((12, 224, ((224, 1), (8, 1), (4, 1)))), ((8, 28), (12, 1)))]

$9^{8}1^{1}$ With the point set $\\{0,1,\dots,72\\}$ partitioned into residue
classes modulo $8$ for $\\{0,1,\dots,71\\}$, and $\\{72\\}$, the design is
generated from

$\\{0,1,5,28,35\\}$, $\\{0,2,13,19,22\\}$, $\\{0,10,25,39,51\\}$,

$\\{0,18,36,54,72\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}72)$ for $x<72$, $72\mapsto
72$, $0\leq j<72$ for the first three blocks, $0\leq j<18$ for the last block.
[(73, ((3, 72, ((72, 1), (1, 1))), (1, 18, ((72, 1), (1, 1)))), ((9, 8), (1,
1)))]

$9^{12}13^{1}$ With the point set $\\{0,1,\dots,120\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,107\\}$, and
$\\{108,109,\dots,120\\}$, the design is generated from

$\\{0,1,4,6,94\\}$, $\\{0,7,37,45,68\\}$, $\\{0,13,57,79,109\\}$,

$\\{0,10,62,97,117\\}$, $\\{0,9,28,67,83\\}$, $\\{0,17,49,82,111\\}$,

$\\{0,27,54,81,120\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}108)$ for $x<108$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+108$ for $108\leq x<120$, $120\mapsto
120$, $0\leq j<108$ for the first six blocks, $0\leq j<27$ for the last block.
[(121, ((6, 108, ((108, 1), (12, 1), (1, 1))), (1, 27, ((108, 1), (12, 1), (1,
1)))), ((9, 12), (13, 1)))]

$9^{16}5^{1}$ With the point set $\\{0,1,\dots,148\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,146,147,148\\}$, the design is generated from

$\\{77,25,52,19,82\\}$, $\\{20,43,30,34,22\\}$, $\\{0,1,50,91,144\\}$,

$\\{0,17,45,83,105\\}$, $\\{0,3,43,62,77\\}$, $\\{0,18,47,73,93\\}$,

$\\{0,7,31,42,107\\}$, $\\{0,36,72,108,148\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+144$ for $144\leq x<148$, $148\mapsto
148$, $0\leq j<144$ for the first seven blocks, $0\leq j<36$ for the last
block.
[(149, ((7, 144, ((144, 1), (4, 1), (1, 1))), (1, 36, ((144, 1), (4, 1), (1,
1)))), ((9, 16), (5, 1)))]

$9^{16}25^{1}$ With the point set $\\{0,1,\dots,168\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,168\\}$, the design is generated from

$\\{162,118,115,88,28\\}$, $\\{86,159,75,12,131\\}$, $\\{99,26,57,79,112\\}$,

$\\{0,4,9,50,129\\}$, $\\{0,7,75,85,162\\}$, $\\{0,2,14,97,118\\}$,

$\\{0,6,35,43,163\\}$, $\\{0,1,18,52,154\\}$, $\\{0,23,62,100,165\\}$,

$\\{0,36,72,108,168\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+144$ for $144\leq x<168$, $168\mapsto
168$, $0\leq j<144$ for the first nine blocks, $0\leq j<36$ for the last
block.
[(169, ((9, 144, ((144, 1), (24, 1), (1, 1))), (1, 36, ((144, 1), (24, 1), (1,
1)))), ((9, 16), (25, 1)))]

$9^{20}17^{1}$ With the point set $\\{0,1,\dots,196\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,196\\}$, the design is generated from

$\\{51,81,35,37,166\\}$, $\\{104,187,125,15,42\\}$, $\\{27,20,88,136,62\\}$,

$\\{0,1,79,82,181\\}$, $\\{0,5,15,38,180\\}$, $\\{0,6,19,37,182\\}$,

$\\{0,4,43,54,127\\}$, $\\{0,8,36,113,122\\}$, $\\{0,17,69,93,125\\}$,

$\\{0,12,34,59,151\\}$, $\\{0,45,90,135,196\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x-180+4j~{}(\mathrm{mod}~{}16))+180$ for $180\leq x<196$,
$196\mapsto 196$, $0\leq j<180$ for the first ten blocks, $0\leq j<45$ for the
last block.
[(197, ((10, 180, ((180, 1), (16, 4), (1, 1))), (1, 45, ((180, 1), (16, 4),
(1, 1)))), ((9, 20), (17, 1)))]

$9^{20}29^{1}$ With the point set $\\{0,1,\dots,208\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,208\\}$, the design is generated from

$\\{180,33,46,103,152\\}$, $\\{25,150,204,8,111\\}$, $\\{114,10,22,146,64\\}$,

$\\{82,68,109,205,47\\}$, $\\{0,3,25,34,186\\}$, $\\{0,10,47,73,182\\}$,

$\\{0,15,33,102,181\\}$, $\\{0,4,11,79,95\\}$, $\\{0,1,59,65,67\\}$,

$\\{0,30,81,127,185\\}$, $\\{0,5,28,137,156\\}$, $\\{0,45,90,135,208\\}$,

$\\{0,36,72,108,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x-180+7j~{}(\mathrm{mod}~{}28))+180$ for $180\leq x<208$,
$208\mapsto 208$, $0\leq j<180$ for the first 11 blocks, $0\leq j<45$ for the
next block, $0\leq j<36$ for the last block.
[(209, ((11, 180, ((180, 1), (28, 7), (1, 1))), (1, 45, ((180, 1), (28, 7),
(1, 1))), (1, 36, ((180, 1), (28, 7), (1, 1)))), ((9, 20), (29, 1)))]

$9^{20}37^{1}$ With the point set $\\{0,1,\dots,216\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,216\\}$, the design is generated from

$\\{0,174,37,52,189\\}$, $\\{53,17,114,121,168\\}$, $\\{46,113,94,2,180\\}$,

$\\{0,134,193,24,101\\}$, $\\{94,85,169,83,156\\}$, $\\{0,8,57,95,129\\}$,

$\\{0,1,99,177,187\\}$, $\\{0,5,130,158,213\\}$, $\\{0,12,150,166,204\\}$,

$\\{0,10,31,63,207\\}$, $\\{0,23,64,89,202\\}$, $\\{0,17,56,162,201\\}$,

$\\{0,45,90,135,216\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+180$ for $180\leq x<216$, $216\mapsto
216$, $0\leq j<180$ for the first 12 blocks, $0\leq j<45$ for the last block.
[(217, ((12, 180, ((180, 1), (36, 1), (1, 1))), (1, 45, ((180, 1), (36, 1),
(1, 1)))), ((9, 20), (37, 1)))]

$9^{20}49^{1}$ With the point set $\\{0,1,\dots,228\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,228\\}$, the design is generated from

$\\{66,60,114,64,165\\}$, $\\{59,219,26,82,75\\}$, $\\{118,115,215,87,21\\}$,

$\\{74,193,95,28,10\\}$, $\\{69,86,190,160,108\\}$, $\\{0,5,13,76,223\\}$,

$\\{0,1,27,62,227\\}$, $\\{0,10,133,148,192\\}$, $\\{0,12,41,65,209\\}$,

$\\{0,14,84,121,199\\}$, $\\{0,11,69,161,195\\}$, $\\{0,38,93,136,181\\}$,

$\\{0,9,34,112,211\\}$, $\\{0,45,90,135,228\\}$, $\\{0,36,72,108,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+180$ for $180\leq x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+216$ for $216\leq x<228$, $228\mapsto
228$, $0\leq j<180$ for the first 13 blocks, $0\leq j<45$ for the next block,
$0\leq j<36$ for the last block.
[(229, ((13, 180, ((180, 1), (36, 1), (12, 1), (1, 1))), (1, 45, ((180, 1),
(36, 1), (12, 1), (1, 1))), (1, 36, ((180, 1), (36, 1), (12, 1), (1, 1)))),
((9, 20), (49, 1)))]

$9^{28}1^{1}$ With the point set $\\{0,1,\dots,252\\}$ partitioned into
residue classes modulo $28$ for $\\{0,1,\dots,251\\}$, and $\\{252\\}$, the
design is generated from

$\\{126,140,248,179,153\\}$, $\\{81,244,212,152,234\\}$,
$\\{204,146,58,65,100\\}$,

$\\{6,234,73,37,22\\}$, $\\{168,220,135,215,211\\}$, $\\{0,1,18,151,174\\}$,

$\\{0,6,54,103,186\\}$, $\\{0,8,20,118,143\\}$, $\\{0,2,61,64,138\\}$,

$\\{0,11,41,111,218\\}$, $\\{0,21,50,94,187\\}$, $\\{0,19,57,147,184\\}$,

$\\{0,63,126,189,252\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}252)$ for $x<252$, $252\mapsto
252$, $0\leq j<252$ for the first 12 blocks, $0\leq j<63$ for the last block.
[(253, ((12, 252, ((252, 1), (1, 1))), (1, 63, ((252, 1), (1, 1)))), ((9, 28),
(1, 1)))]

$10^{10}18^{1}$ With the point set $\\{0,1,\dots,117\\}$ partitioned into
residue classes modulo $9$ for $\\{0,1,\dots,89\\}$, $\\{90,91,\dots,99\\}$,
and $\\{100,101,\dots,117\\}$, the design is generated from

$\\{23,19,29,81,16\\}$, $\\{24,20,30,82,17\\}$, $\\{53,101,36,48,99\\}$,

$\\{54,102,37,49,90\\}$, $\\{109,48,4,64,15\\}$, $\\{0,8,43,90,111\\}$,

$\\{0,26,59,75,94\\}$, $\\{1,15,35,61,115\\}$, $\\{0,21,22,61,113\\}$,

$\\{0,1,20,76,114\\}$, $\\{0,2,50,69,100\\}$, $\\{0,23,31,66,95\\}$,

$\\{0,37,79,97,106\\}$, $\\{0,29,51,53,108\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}90)$ for $x<90$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}10))+90$ for $90\leq x<100$,
$x\mapsto(x-100+2j~{}(\mathrm{mod}~{}18))+100$ for $x\geq 100$, $0\leq j<45$.
[(118, ((14, 45, ((90, 2), (10, 2), (18, 2)))), ((10, 9), (10, 1), (18, 1)))]

$10^{20}38^{1}$ With the point set $\\{0,1,\dots,237\\}$ partitioned into
residue classes modulo $19$ for $\\{0,1,\dots,189\\}$,
$\\{190,191,\dots,199\\}$, and $\\{200,201,\dots,237\\}$, the design is
generated from

$\\{150,141,128,72,168\\}$, $\\{108,150,9,191,134\\}$,
$\\{236,60,106,188,143\\}$,

$\\{71,174,206,36,8\\}$, $\\{82,155,154,187,232\\}$,
$\\{118,200,149,63,74\\}$,

$\\{0,2,5,142,178\\}$, $\\{0,23,77,120,205\\}$, $\\{0,8,74,198,225\\}$,

$\\{0,6,21,132,201\\}$, $\\{0,7,68,156,216\\}$, $\\{0,25,92,131,210\\}$,

$\\{0,4,143,199,219\\}$, $\\{0,10,30,90,119\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}190)$ for $x<190$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}10))+190$ for $190\leq x<200$,
$x\mapsto(x-200+j~{}(\mathrm{mod}~{}38))+200$ for $x\geq 200$, $0\leq j<190$.
[(238, ((14, 190, ((190, 1), (10, 1), (38, 1)))), ((10, 19), (10, 1), (38,
1)))]

$11^{20}19^{1}$ With the point set $\\{0,1,\dots,238\\}$ partitioned into
residue classes modulo $19$ for $\\{0,1,\dots,208\\}$,
$\\{209,210,\dots,219\\}$, and $\\{220,221,\dots,238\\}$, the design is
generated from

$\\{200,139,116,210,225\\}$, $\\{237,31,127,141,191\\}$,
$\\{94,164,203,0,35\\}$,

$\\{97,113,215,101,10\\}$, $\\{111,131,162,140,167\\}$,
$\\{220,89,135,122,37\\}$,

$\\{0,10,25,166,210\\}$, $\\{0,7,67,104,130\\}$, $\\{0,8,40,128,222\\}$,

$\\{0,21,92,175,232\\}$, $\\{0,1,18,66,108\\}$, $\\{0,11,69,93,147\\}$,

$\\{0,2,30,74,77\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}209)$ for $x<209$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}11))+209$ for $209\leq x<220$,
$x\mapsto(x-220+j~{}(\mathrm{mod}~{}19))+220$ for $x\geq 220$, $0\leq j<209$.
[(239, ((13, 209, ((209, 1), (11, 1), (19, 1)))), ((11, 19), (11, 1), (19,
1)))]

$12^{5}8^{1}$ With the point set $\\{0,1,\dots,67\\}$ partitioned into residue
classes modulo $5$ for $\\{0,1,\dots,59\\}$, and $\\{60,61,\dots,67\\}$, the
design is generated from

$\\{0,2,49,51,64\\}$, $\\{0,1,7,33,59\\}$, $\\{0,4,38,41,57\\}$,

$\\{0,18,19,26,32\\}$, $\\{0,9,13,31,62\\}$, $\\{0,3,6,17,65\\}$,

$\\{0,8,22,29,60\\}$, $\\{0,11,42,58,61\\}$, $\\{1,18,22,39,55\\}$,

$\\{1,2,30,53,66\\}$, $\\{0,16,39,43,67\\}$, $\\{1,15,34,43,61\\}$,

$\\{0,12,24,36,48\\}$

by the mapping: $x\mapsto x+4j~{}(\mathrm{mod}~{}60)$ for $x<60$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}5))+60$ for $60\leq x<65$,
$x\mapsto(x-65+j~{}(\mathrm{mod}~{}3))+65$ for $x\geq 65$, $0\leq j<15$ for
the first 12 blocks; $x\mapsto x+j~{}(\mathrm{mod}~{}60)$ for $x<60$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}5))+60$ for $60\leq x<65$,
$x\mapsto(x-65+j~{}(\mathrm{mod}~{}3))+65$ for $x\geq 65$, $0\leq j<12$ for
the last block.
[(68, ((12, 15, ((60, 4), (5, 1), (3, 1))), (1, 12, ((60, 1), (5, 1), (3,
1)))), ((12, 5), (8, 1)))]

$12^{10}8^{1}$ With the point set $\\{0,1,\dots,127\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,127\\}$, the design is generated from

$\\{21,125,79,46,64\\}$, $\\{105,124,66,107,112\\}$, $\\{0,8,19,36,107\\}$,

$\\{0,1,23,27,86\\}$, $\\{0,3,12,54,68\\}$, $\\{0,6,37,53,82\\}$,

$\\{0,24,48,72,96\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+120$ for $x\geq 120$, $0\leq j<120$ for
the first six blocks, $0\leq j<24$ for the last block.
[(128, ((6, 120, ((120, 1), (8, 1))), (1, 24, ((120, 1), (8, 1)))), ((12, 10),
(8, 1)))]

$12^{10}16^{1}$ With the point set $\\{0,1,\dots,135\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,135\\}$, the design is generated from

$\\{49,118,74,134,37\\}$, $\\{69,129,56,83,65\\}$, $\\{0,5,28,73,120\\}$,

$\\{0,2,36,101,125\\}$, $\\{0,3,32,38,49\\}$, $\\{0,1,43,59,67\\}$,

$\\{0,7,22,63,94\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x-120+2j~{}(\mathrm{mod}~{}16))+120$ for $x\geq 120$, $0\leq j<120$.
[(136, ((7, 120, ((120, 1), (16, 2)))), ((12, 10), (16, 1)))]

$12^{10}28^{1}$ With the point set $\\{0,1,\dots,147\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,119\\}$, and
$\\{120,121,\dots,147\\}$, the design is generated from

$\\{119,25,77,78,84\\}$, $\\{109,138,92,90,34\\}$, $\\{0,3,25,34,144\\}$,

$\\{0,5,18,92,139\\}$, $\\{0,12,69,83,138\\}$, $\\{0,8,23,99,132\\}$,

$\\{0,4,36,47,135\\}$, $\\{0,16,54,81,122\\}$, $\\{0,24,48,72,96\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}120)$ for $x<120$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+120$ for $120\leq x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+144$ for $x\geq 144$, $0\leq j<120$ for
the first eight blocks, $0\leq j<24$ for the last block.
[(148, ((8, 120, ((120, 1), (24, 1), (4, 1))), (1, 24, ((120, 1), (24, 1), (4,
1)))), ((12, 10), (28, 1)))]

$12^{11}20^{1}$ With the point set $\\{0,1,\dots,151\\}$ partitioned into
residue classes modulo $11$ for $\\{0,1,\dots,131\\}$, and
$\\{132,133,\dots,151\\}$, the design is generated from

$\\{17,144,63,128,86\\}$, $\\{34,151,0,113,107\\}$, $\\{0,1,51,58,132\\}$,

$\\{0,5,14,119,135\\}$, $\\{0,15,45,62,133\\}$, $\\{0,3,38,64,92\\}$,

$\\{0,2,12,95,103\\}$, $\\{0,4,24,84,100\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}132)$ for $x<132$,
$x\mapsto(x-132+5j~{}(\mathrm{mod}~{}20))+132$ for $x\geq 132$, $0\leq j<132$.
[(152, ((8, 132, ((132, 1), (20, 5)))), ((12, 11), (20, 1)))]

$12^{12}4^{1}$ With the point set $\\{0,1,\dots,147\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,146,147\\}$, the design is generated from

$\\{145,26,49,15,12\\}$, $\\{104,62,16,77,97\\}$, $\\{0,1,55,65,71\\}$,

$\\{0,4,25,33,91\\}$, $\\{0,9,28,50,68\\}$, $\\{0,2,32,49,101\\}$,

$\\{0,5,31,44,82\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+144$ for $x\geq 144$, $0\leq j<144$.
[(148, ((7, 144, ((144, 1), (4, 1)))), ((12, 12), (4, 1)))]

$12^{12}24^{1}$ With the point set $\\{0,1,\dots,167\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,167\\}$, the design is generated from

$\\{89,110,157,118,87\\}$, $\\{154,46,61,122,66\\}$, $\\{113,33,47,162,79\\}$,

$\\{0,1,101,134,151\\}$, $\\{0,19,71,109,157\\}$, $\\{0,17,70,119,147\\}$,

$\\{0,6,13,22,63\\}$, $\\{0,4,30,69,97\\}$, $\\{0,3,40,58,85\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+144$ for $x\geq 144$, $0\leq j<144$.
[(168, ((9, 144, ((144, 1), (24, 1)))), ((12, 12), (24, 1)))]

$12^{13}8^{1}$ With the point set $\\{0,1,\dots,163\\}$ partitioned into
residue classes modulo $13$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,163\\}$, the design is generated from

$\\{17,151,107,23,126\\}$, $\\{105,87,90,94,151\\}$, $\\{0,1,34,43,157\\}$,

$\\{0,23,54,81,156\\}$, $\\{0,2,40,76,108\\}$, $\\{0,5,21,35,94\\}$,

$\\{0,10,55,79,96\\}$, $\\{0,8,20,71,127\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x-156+2j~{}(\mathrm{mod}~{}8))+156$ for $x\geq 156$, $0\leq j<156$.
[(164, ((8, 156, ((156, 1), (8, 2)))), ((12, 13), (8, 1)))]

$12^{13}28^{1}$ With the point set $\\{0,1,\dots,183\\}$ partitioned into
residue classes modulo $13$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,183\\}$, the design is generated from

$\\{56,119,9,42,110\\}$, $\\{16,152,65,60,166\\}$, $\\{73,164,30,104,62\\}$,

$\\{0,1,128,135,170\\}$, $\\{0,6,25,111,180\\}$, $\\{0,2,12,96,120\\}$,

$\\{0,4,27,61,165\\}$, $\\{0,17,35,76,106\\}$, $\\{0,3,103,119,175\\}$,

$\\{0,8,83,98,171\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x-156+2j~{}(\mathrm{mod}~{}24))+156$ for $156\leq x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+180$ for $x\geq 180$, $0\leq j<156$.
[(184, ((10, 156, ((156, 1), (24, 2), (4, 1)))), ((12, 13), (28, 1)))]

$12^{14}32^{1}$ With the point set $\\{0,1,\dots,199\\}$ partitioned into
residue classes modulo $14$ for $\\{0,1,\dots,167\\}$, and
$\\{168,169,\dots,199\\}$, the design is generated from

$\\{189,166,52,157,107\\}$, $\\{148,4,140,115,100\\}$,
$\\{84,95,189,111,20\\}$,

$\\{115,117,41,138,80\\}$, $\\{0,1,31,117,180\\}$, $\\{0,5,41,67,189\\}$,

$\\{0,12,34,80,99\\}$, $\\{0,6,44,89,188\\}$, $\\{0,18,61,108,175\\}$,

$\\{0,20,49,115,196\\}$, $\\{0,3,7,158,197\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}168)$ for $x<168$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+168$ for $168\leq x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+192$ for $x\geq 192$, $0\leq j<168$.
[(200, ((11, 168, ((168, 1), (24, 1), (8, 1)))), ((12, 14), (32, 1)))]

$12^{15}8^{1}$ With the point set $\\{0,1,\dots,187\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,187\\}$, the design is generated from

$\\{175,18,106,11,128\\}$, $\\{67,66,149,153,94\\}$, $\\{0,2,5,11,181\\}$,

$\\{0,13,62,127,180\\}$, $\\{0,19,44,100,151\\}$, $\\{0,8,18,39,148\\}$,

$\\{0,12,26,64,138\\}$, $\\{0,24,57,103,146\\}$, $\\{0,17,37,78,113\\}$,

$\\{0,36,72,108,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x-180+2j~{}(\mathrm{mod}~{}8))+180$ for $x\geq 180$, $0\leq j<180$
for the first nine blocks, $0\leq j<36$ for the last block.
[(188, ((9, 180, ((180, 1), (8, 2))), (1, 36, ((180, 1), (8, 2)))), ((12, 15),
(8, 1)))]

$12^{15}16^{1}$ With the point set $\\{0,1,\dots,195\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,195\\}$, the design is generated from

$\\{59,19,60,172,189\\}$, $\\{193,133,171,140,54\\}$, $\\{9,133,18,15,141\\}$,

$\\{72,150,179,91,187\\}$, $\\{0,10,109,137,184\\}$, $\\{0,5,47,111,134\\}$,

$\\{0,11,33,77,91\\}$, $\\{0,4,20,145,163\\}$, $\\{0,2,26,98,130\\}$,

$\\{0,12,25,61,95\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+180$ for $180\leq x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+192$ for $x\geq 192$, $0\leq j<180$.
[(196, ((10, 180, ((180, 1), (12, 1), (4, 1)))), ((12, 15), (16, 1)))]

$12^{15}28^{1}$ With the point set $\\{0,1,\dots,207\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,207\\}$, the design is generated from

$\\{203,2,113,132,103\\}$, $\\{8,15,188,122,161\\}$,
$\\{170,161,200,43,48\\}$,

$\\{29,205,116,67,46\\}$, $\\{0,1,3,98,183\\}$, $\\{0,13,54,115,185\\}$,

$\\{0,23,74,117,180\\}$, $\\{0,6,31,140,154\\}$, $\\{0,4,22,125,160\\}$,

$\\{0,8,64,76,92\\}$, $\\{0,11,44,91,143\\}$, $\\{0,36,72,108,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x-180+7j~{}(\mathrm{mod}~{}28))+180$ for $x\geq 180$, $0\leq j<180$
for the first 11 blocks, $0\leq j<36$ for the last block.
[(208, ((11, 180, ((180, 1), (28, 7))), (1, 36, ((180, 1), (28, 7)))), ((12,
15), (28, 1)))]

$12^{15}36^{1}$ With the point set $\\{0,1,\dots,215\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,215\\}$, the design is generated from

$\\{197,72,69,70,47\\}$, $\\{160,173,78,127,71\\}$, $\\{210,65,105,129,36\\}$,

$\\{141,68,200,60,136\\}$, $\\{8,174,181,42,73\\}$, $\\{0,11,62,83,125\\}$,

$\\{0,17,36,54,74\\}$, $\\{0,6,58,67,188\\}$, $\\{0,10,80,164,215\\}$,

$\\{0,4,43,152,198\\}$, $\\{0,27,77,121,183\\}$, $\\{0,12,47,139,196\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+180$ for $x\geq 180$, $0\leq j<180$.
[(216, ((12, 180, ((180, 1), (36, 1)))), ((12, 15), (36, 1)))]

$12^{15}48^{1}$ With the point set $\\{0,1,\dots,227\\}$ partitioned into
residue classes modulo $15$ for $\\{0,1,\dots,179\\}$, and
$\\{180,181,\dots,227\\}$, the design is generated from

$\\{86,149,8,196,54\\}$, $\\{164,96,77,148,221\\}$, $\\{79,123,56,190,39\\}$,

$\\{157,219,132,153,160\\}$, $\\{124,137,115,5,202\\}$,
$\\{11,38,92,222,58\\}$,

$\\{0,1,104,122,185\\}$, $\\{0,29,64,143,192\\}$, $\\{0,11,49,73,138\\}$,

$\\{0,5,55,129,181\\}$, $\\{0,6,86,98,180\\}$, $\\{0,14,57,83,215\\}$,

$\\{0,2,33,172,205\\}$, $\\{0,36,72,108,144\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}180)$ for $x<180$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+180$ for $180\leq x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+216$ for $x\geq 216$, $0\leq j<180$ for
the first 13 blocks, $0\leq j<36$ for the last block.
[(228, ((13, 180, ((180, 1), (36, 1), (12, 1))), (1, 36, ((180, 1), (36, 1),
(12, 1)))), ((12, 15), (48, 1)))]

$12^{16}20^{1}$ With the point set $\\{0,1,\dots,211\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,211\\}$, the design is generated from

$\\{193,106,109,79,37\\}$, $\\{7,209,109,96,134\\}$, $\\{45,34,171,163,88\\}$,

$\\{204,35,87,182,66\\}$, $\\{0,1,34,36,207\\}$, $\\{0,37,87,136,200\\}$,

$\\{0,12,40,59,151\\}$, $\\{0,7,17,77,148\\}$, $\\{0,5,67,106,124\\}$,

$\\{0,4,24,82,170\\}$, $\\{0,6,15,29,113\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+192$ for $192\leq x<208$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+208$ for $x\geq 208$, $0\leq j<192$.
[(212, ((11, 192, ((192, 1), (16, 1), (4, 1)))), ((12, 16), (20, 1)))]

$12^{16}40^{1}$ With the point set $\\{0,1,\dots,231\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,191\\}$, and
$\\{192,193,\dots,231\\}$, the design is generated from

$\\{11,53,203,121,42\\}$, $\\{2,228,36,150,131\\}$, $\\{95,103,90,164,83\\}$,

$\\{63,206,101,3,91\\}$, $\\{153,96,215,180,139\\}$,
$\\{152,87,153,223,15\\}$,

$\\{0,6,153,162,229\\}$, $\\{0,17,109,134,202\\}$, $\\{0,15,37,77,136\\}$,

$\\{0,2,103,107,220\\}$, $\\{0,18,53,159,205\\}$, $\\{0,3,49,70,197\\}$,

$\\{0,23,47,73,163\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}192)$ for $x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}32))+192$ for $192\leq x<224$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+224$ for $x\geq 224$, $0\leq j<192$.
[(232, ((13, 192, ((192, 1), (32, 1), (8, 1)))), ((12, 16), (40, 1)))]

$12^{17}4^{1}$ With the point set $\\{0,1,\dots,207\\}$ partitioned into
residue classes modulo $17$ for $\\{0,1,\dots,203\\}$, and
$\\{204,205,206,207\\}$, the design is generated from

$\\{136,64,203,52,12\\}$, $\\{81,42,4,11,167\\}$, $\\{152,107,106,103,133\\}$,

$\\{200,59,204,150,5\\}$, $\\{0,15,35,71,161\\}$, $\\{0,11,25,98,160\\}$,

$\\{0,16,37,112,144\\}$, $\\{0,2,10,111,140\\}$, $\\{0,6,28,89,122\\}$,

$\\{0,5,23,47,104\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}204)$ for $x<204$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+204$ for $x\geq 204$, $0\leq j<204$.
[(208, ((10, 204, ((204, 1), (4, 1)))), ((12, 17), (4, 1)))]

$12^{17}24^{1}$ With the point set $\\{0,1,\dots,227\\}$ partitioned into
residue classes modulo $17$ for $\\{0,1,\dots,203\\}$, and
$\\{204,205,\dots,227\\}$, the design is generated from

$\\{188,218,134,75,37\\}$, $\\{58,221,176,62,192\\}$,
$\\{93,13,133,165,102\\}$,

$\\{149,66,113,188,87\\}$, $\\{91,179,62,18,67\\}$, $\\{0,13,48,94,108\\}$,

$\\{0,2,12,79,140\\}$, $\\{0,1,19,56,210\\}$, $\\{0,3,23,182,204\\}$,

$\\{0,11,146,174,211\\}$, $\\{0,8,50,65,219\\}$, $\\{0,6,33,104,111\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}204)$ for $x<204$,
$x\mapsto(x-204+2j~{}(\mathrm{mod}~{}24))+204$ for $x\geq 204$, $0\leq j<204$.
[(228, ((12, 204, ((204, 1), (24, 2)))), ((12, 17), (24, 1)))]

$12^{17}44^{1}$ With the point set $\\{0,1,\dots,247\\}$ partitioned into
residue classes modulo $17$ for $\\{0,1,\dots,203\\}$, and
$\\{204,205,\dots,247\\}$, the design is generated from

$\\{119,149,226,160,141\\}$, $\\{208,52,201,121,163\\}$,
$\\{137,237,133,162,84\\}$,

$\\{187,133,229,69,75\\}$, $\\{82,98,19,1,203\\}$, $\\{148,225,19,180,89\\}$,

$\\{0,5,45,76,207\\}$, $\\{0,9,66,139,240\\}$, $\\{0,13,27,50,241\\}$,

$\\{0,3,15,39,87\\}$, $\\{0,1,61,89,96\\}$, $\\{0,44,90,142,206\\}$,

$\\{0,21,47,103,230\\}$, $\\{0,10,104,137,215\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}204)$ for $x<204$,
$x\mapsto(x-204+3j~{}(\mathrm{mod}~{}36))+204$ for $204\leq x<240$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}8))+240$ for $x\geq 240$, $0\leq j<204$.
[(248, ((14, 204, ((204, 1), (36, 3), (8, 2)))), ((12, 17), (44, 1)))]

$12^{18}8^{1}$ With the point set $\\{0,1,\dots,223\\}$ partitioned into
residue classes modulo $18$ for $\\{0,1,\dots,215\\}$, and
$\\{216,217,\dots,223\\}$, the design is generated from

$\\{46,40,182,140,125\\}$, $\\{222,76,37,62,74\\}$, $\\{73,76,175,131,84\\}$,

$\\{62,89,58,63,108\\}$, $\\{0,7,66,206,221\\}$, $\\{0,13,81,119,141\\}$,

$\\{0,23,51,118,183\\}$, $\\{0,9,61,96,139\\}$, $\\{0,21,53,124,154\\}$,

$\\{0,29,63,111,175\\}$, $\\{0,16,40,89,109\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}216)$ for $x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+216$ for $x\geq 216$, $0\leq j<216$.
[(224, ((11, 216, ((216, 1), (8, 1)))), ((12, 18), (8, 1)))]

$12^{18}28^{1}$ With the point set $\\{0,1,\dots,243\\}$ partitioned into
residue classes modulo $18$ for $\\{0,1,\dots,215\\}$, and
$\\{216,217,\dots,243\\}$, the design is generated from

$\\{243,11,196,81,2\\}$, $\\{57,72,83,208,206\\}$, $\\{98,140,133,117,186\\}$,

$\\{64,171,39,181,26\\}$, $\\{177,115,55,82,219\\}$, $\\{0,1,4,188,196\\}$,

$\\{0,17,66,114,158\\}$, $\\{0,37,76,133,176\\}$, $\\{0,5,78,165,226\\}$,

$\\{0,6,47,110,222\\}$, $\\{0,30,85,135,219\\}$, $\\{0,14,59,127,225\\}$,

$\\{0,12,130,164,227\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}216)$ for $x<216$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+216$ for $216\leq x<240$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+240$ for $x\geq 240$, $0\leq j<216$.
[(244, ((13, 216, ((216, 1), (24, 1), (4, 1)))), ((12, 18), (28, 1)))]

$12^{18}48^{1}$ With the point set $\\{0,1,\dots,263\\}$ partitioned into
residue classes modulo $18$ for $\\{0,1,\dots,215\\}$, and
$\\{216,217,\dots,263\\}$, the design is generated from

$\\{139,181,20,168,116\\}$, $\\{165,247,43,44,83\\}$,
$\\{115,257,202,17,31\\}$,

$\\{67,158,216,75,72\\}$, $\\{109,229,28,102,143\\}$,
$\\{246,137,86,165,118\\}$,

$\\{0,30,63,143,245\\}$, $\\{0,12,100,117,235\\}$, $\\{0,6,112,179,261\\}$,

$\\{0,10,21,71,178\\}$, $\\{0,2,22,78,192\\}$, $\\{0,27,85,154,220\\}$,

$\\{0,15,64,139,228\\}$, $\\{0,4,70,163,230\\}$, $\\{0,9,44,200,224\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}216)$ for $x<216$,
$x\mapsto(x-216+2j~{}(\mathrm{mod}~{}48))+216$ for $x\geq 216$, $0\leq j<216$.
[(264, ((15, 216, ((216, 1), (48, 2)))), ((12, 18), (48, 1)))]

$12^{19}32^{1}$ With the point set $\\{0,1,\dots,259\\}$ partitioned into
residue classes modulo $19$ for $\\{0,1,\dots,227\\}$, and
$\\{228,229,\dots,259\\}$, the design is generated from

$\\{185,139,30,231,216\\}$, $\\{245,50,213,48,35\\}$,
$\\{198,115,190,54,151\\}$,

$\\{259,99,25,70,204\\}$, $\\{184,241,99,113,122\\}$,
$\\{83,32,162,161,172\\}$,

$\\{0,5,27,142,232\\}$, $\\{0,17,58,175,234\\}$, $\\{0,21,55,162,230\\}$,

$\\{0,26,59,185,228\\}$, $\\{0,20,64,101,168\\}$, $\\{0,6,24,54,106\\}$,

$\\{0,3,28,35,138\\}$, $\\{0,4,16,72,112\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}228)$ for $x<228$,
$x\mapsto(x-228+8j~{}(\mathrm{mod}~{}32))+228$ for $x\geq 228$, $0\leq j<228$.
[(260, ((14, 228, ((228, 1), (32, 8)))), ((12, 19), (32, 1)))]

$12^{19}52^{1}$ With the point set $\\{0,1,\dots,279\\}$ partitioned into
residue classes modulo $19$ for $\\{0,1,\dots,227\\}$, and
$\\{228,229,\dots,279\\}$, the design is generated from

$\\{250,205,227,108,200\\}$, $\\{273,92,45,175,2\\}$,
$\\{220,21,239,115,12\\}$,

$\\{261,7,144,207,118\\}$, $\\{82,5,3,132,240\\}$, $\\{111,272,98,31,77\\}$,

$\\{0,1,7,212,257\\}$, $\\{0,3,187,217,236\\}$, $\\{0,10,61,163,276\\}$,

$\\{0,12,36,71,156\\}$, $\\{0,15,60,93,147\\}$, $\\{0,4,66,179,258\\}$,

$\\{0,37,106,158,230\\}$, $\\{0,8,39,64,112\\}$, $\\{0,32,74,142,275\\}$,

$\\{0,18,58,146,255\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}228)$ for $x<228$,
$x\mapsto(x-228+4j~{}(\mathrm{mod}~{}48))+228$ for $228\leq x<276$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+276$ for $x\geq 276$, $0\leq j<228$.
[(280, ((16, 228, ((228, 1), (48, 4), (4, 1)))), ((12, 19), (52, 1)))]

$12^{20}8^{1}$ With the point set $\\{0,1,\dots,247\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,239\\}$, and
$\\{240,241,\dots,247\\}$, the design is generated from

$\\{33,245,148,94,64\\}$, $\\{7,223,176,191,134\\}$, $\\{160,219,15,56,6\\}$,

$\\{16,140,28,26,3\\}$, $\\{81,145,92,7,213\\}$, $\\{0,45,110,162,240\\}$,

$\\{0,16,33,91,174\\}$, $\\{0,38,87,131,177\\}$, $\\{0,7,35,129,168\\}$,

$\\{0,1,4,171,222\\}$, $\\{0,6,14,43,148\\}$, $\\{0,5,26,81,178\\}$,

$\\{0,48,96,144,192\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}240)$ for $x<240$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+240$ for $x\geq 240$, $0\leq j<240$ for
the first 12 blocks, $0\leq j<48$ for the last block.
[(248, ((12, 240, ((240, 1), (8, 1))), (1, 48, ((240, 1), (8, 1)))), ((12,
20), (8, 1)))]

$12^{21}20^{1}$ With the point set $\\{0,1,\dots,271\\}$ partitioned into
residue classes modulo $21$ for $\\{0,1,\dots,251\\}$, and
$\\{252,253,\dots,271\\}$, the design is generated from

$\\{113,94,74,217,245\\}$, $\\{215,76,108,242,143\\}$,
$\\{61,249,149,258,203\\}$,

$\\{61,53,240,197,38\\}$, $\\{247,241,217,47,250\\}$,
$\\{100,153,23,151,83\\}$,

$\\{0,1,79,90,265\\}$, $\\{0,34,71,169,264\\}$, $\\{0,7,55,102,193\\}$,

$\\{0,16,38,112,141\\}$, $\\{0,5,31,41,196\\}$, $\\{0,12,25,69,131\\}$,

$\\{0,40,85,177,252\\}$, $\\{0,4,18,176,262\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}252)$ for $x<252$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+252$ for $252\leq x<264$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}8))+264$ for $x\geq 264$, $0\leq j<252$.
[(272, ((14, 252, ((252, 1), (12, 1), (8, 2)))), ((12, 21), (20, 1)))]

$12^{21}40^{1}$ With the point set $\\{0,1,\dots,291\\}$ partitioned into
residue classes modulo $21$ for $\\{0,1,\dots,251\\}$, and
$\\{252,253,\dots,291\\}$, the design is generated from

$\\{142,36,282,31,124\\}$, $\\{251,168,59,58,102\\}$,
$\\{3,257,163,74,214\\}$,

$\\{7,177,4,56,40\\}$, $\\{22,16,161,9,200\\}$, $\\{193,283,18,94,63\\}$,

$\\{156,183,280,247,191\\}$, $\\{0,2,11,25,288\\}$, $\\{0,10,34,158,190\\}$,

$\\{0,19,57,127,174\\}$, $\\{0,12,67,224,283\\}$, $\\{0,30,120,166,272\\}$,

$\\{0,22,75,226,267\\}$, $\\{0,15,73,102,187\\}$, $\\{0,4,133,202,262\\}$,

$\\{0,17,37,171,280\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}252)$ for $x<252$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+252$ for $252\leq x<288$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+288$ for $x\geq 288$, $0\leq j<252$.
[(292, ((16, 252, ((252, 1), (36, 1), (4, 1)))), ((12, 21), (40, 1)))]

$12^{21}60^{1}$ With the point set $\\{0,1,\dots,311\\}$ partitioned into
residue classes modulo $21$ for $\\{0,1,\dots,251\\}$, and
$\\{252,253,\dots,311\\}$, the design is generated from

$\\{91,300,131,149,61\\}$, $\\{135,174,260,231,203\\}$,
$\\{134,291,180,213,89\\}$,

$\\{84,239,52,293,101\\}$, $\\{0,119,7,120,108\\}$, $\\{53,253,30,140,178\\}$,

$\\{95,154,230,262,45\\}$, $\\{269,243,94,107,189\\}$, $\\{0,2,37,43,303\\}$,

$\\{0,3,51,55,75\\}$, $\\{0,9,36,83,190\\}$, $\\{0,25,85,208,271\\}$,

$\\{0,16,93,146,265\\}$, $\\{0,10,90,121,274\\}$, $\\{0,19,153,179,286\\}$,

$\\{0,8,22,86,276\\}$, $\\{0,5,61,163,306\\}$, $\\{0,15,152,186,300\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}252)$ for $x<252$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+252$ for $252\leq x<288$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}24))+288$ for $x\geq 288$, $0\leq j<252$.
[(312, ((18, 252, ((252, 1), (36, 1), (24, 2)))), ((12, 21), (60, 1)))]

$12^{22}4^{1}$ With the point set $\\{0,1,\dots,267\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,263\\}$, and
$\\{264,265,266,267\\}$, the design is generated from

$\\{210,229,3,186,158\\}$, $\\{8,3,149,242,134\\}$,
$\\{122,200,20,223,164\\}$,

$\\{187,235,101,95,238\\}$, $\\{108,76,155,126,50\\}$, $\\{0,1,63,70,264\\}$,

$\\{0,2,11,106,254\\}$, $\\{0,8,49,83,174\\}$, $\\{0,4,35,100,117\\}$,

$\\{0,27,72,112,149\\}$, $\\{0,13,33,107,210\\}$, $\\{0,14,53,150,218\\}$,

$\\{0,16,80,135,191\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}264)$ for $x<264$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+264$ for $x\geq 264$, $0\leq j<264$.
[(268, ((13, 264, ((264, 1), (4, 1)))), ((12, 22), (4, 1)))]

$12^{22}24^{1}$ With the point set $\\{0,1,\dots,287\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,263\\}$, and
$\\{264,265,\dots,287\\}$, the design is generated from

$\\{55,200,198,170,123\\}$, $\\{189,100,151,214,260\\}$,
$\\{14,257,196,181,185\\}$,

$\\{173,258,39,282,95\\}$, $\\{215,73,123,175,209\\}$,
$\\{145,228,199,88,285\\}$,

$\\{87,107,74,0,205\\}$, $\\{0,1,8,49,248\\}$, $\\{0,31,84,127,200\\}$,

$\\{0,5,113,125,152\\}$, $\\{0,14,173,209,280\\}$, $\\{0,10,80,174,282\\}$,

$\\{0,18,37,99,222\\}$, $\\{0,9,206,238,279\\}$, $\\{0,3,106,129,271\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}264)$ for $x<264$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+264$ for $x\geq 264$, $0\leq j<264$.
[(288, ((15, 264, ((264, 1), (24, 1)))), ((12, 22), (24, 1)))]

$12^{22}44^{1}$ With the point set $\\{0,1,\dots,307\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,263\\}$, and
$\\{264,265,\dots,307\\}$, the design is generated from

$\\{225,105,169,186,229\\}$, $\\{145,116,30,196,223\\}$,
$\\{297,250,252,1,173\\}$,

$\\{241,264,151,259,240\\}$, $\\{238,231,76,137,205\\}$,
$\\{78,28,266,245,145\\}$,

$\\{70,269,123,11,39\\}$, $\\{0,3,8,232,275\\}$, $\\{0,6,131,201,279\\}$,

$\\{0,25,99,141,277\\}$, $\\{0,10,46,58,192\\}$, $\\{0,9,96,145,169\\}$,

$\\{0,20,54,111,300\\}$, $\\{0,16,37,159,294\\}$, $\\{0,14,55,226,305\\}$,

$\\{0,30,75,181,289\\}$, $\\{0,11,76,138,161\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}264)$ for $x<264$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+264$ for $264\leq x<288$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+288$ for $288\leq x<300$,
$x\mapsto(x-300+j~{}(\mathrm{mod}~{}8))+300$ for $x\geq 300$, $0\leq j<264$.
[(308, ((17, 264, ((264, 1), (24, 1), (12, 1), (8, 1)))), ((12, 22), (44,
1)))]

$12^{22}64^{1}$ With the point set $\\{0,1,\dots,327\\}$ partitioned into
residue classes modulo $22$ for $\\{0,1,\dots,263\\}$, and
$\\{264,265,\dots,327\\}$, the design is generated from

$\\{216,50,184,145,131\\}$, $\\{256,319,162,149,192\\}$,
$\\{248,317,84,11,67\\}$,

$\\{278,92,152,153,102\\}$, $\\{177,287,171,162,173\\}$,
$\\{155,202,324,85,184\\}$,

$\\{291,58,27,95,6\\}$, $\\{70,37,1,185,269\\}$, $\\{50,267,140,62,4\\}$,

$\\{0,3,155,259,323\\}$, $\\{0,23,146,238,301\\}$, $\\{0,34,79,142,309\\}$,

$\\{0,20,77,125,197\\}$, $\\{0,24,86,127,182\\}$, $\\{0,35,111,224,280\\}$,

$\\{0,25,84,126,294\\}$, $\\{0,7,131,150,290\\}$, $\\{0,16,135,226,304\\}$,

$\\{0,28,93,190,296\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}264)$ for $x<264$,
$x\mapsto(x-264+2j~{}(\mathrm{mod}~{}48))+264$ for $264\leq x<312$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+312$ for $312\leq x<324$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+324$ for $x\geq 324$, $0\leq j<264$.
[(328, ((19, 264, ((264, 1), (48, 2), (12, 1), (4, 1)))), ((12, 22), (64,
1)))]

$12^{23}28^{1}$ With the point set $\\{0,1,\dots,303\\}$ partitioned into
residue classes modulo $23$ for $\\{0,1,\dots,275\\}$, and
$\\{276,277,\dots,303\\}$, the design is generated from

$\\{269,101,208,67,10\\}$, $\\{49,186,114,147,207\\}$,
$\\{124,51,282,214,205\\}$,

$\\{194,294,19,48,241\\}$, $\\{8,274,277,85,151\\}$, $\\{300,33,70,95,76\\}$,

$\\{0,1,3,14,278\\}$, $\\{0,5,119,126,276\\}$, $\\{0,15,41,246,281\\}$,

$\\{0,4,22,170,194\\}$, $\\{0,27,76,116,218\\}$, $\\{0,20,48,151,245\\}$,

$\\{0,8,50,209,221\\}$, $\\{0,32,70,129,181\\}$, $\\{0,16,100,136,180\\}$,

$\\{0,35,88,144,212\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}276)$ for $x<276$,
$x\mapsto(x-276+7j~{}(\mathrm{mod}~{}28))+276$ for $x\geq 276$, $0\leq j<276$.
[(304, ((16, 276, ((276, 1), (28, 7)))), ((12, 23), (28, 1)))]

$12^{23}48^{1}$ With the point set $\\{0,1,\dots,323\\}$ partitioned into
residue classes modulo $23$ for $\\{0,1,\dots,275\\}$, and
$\\{276,277,\dots,323\\}$, the design is generated from

$\\{45,3,146,197,315\\}$, $\\{73,78,276,29,255\\}$, $\\{109,99,92,90,121\\}$,

$\\{268,64,19,192,102\\}$, $\\{312,56,133,203,67\\}$,
$\\{156,3,281,88,273\\}$,

$\\{302,23,27,98,210\\}$, $\\{6,86,21,85,242\\}$, $\\{0,3,154,263,288\\}$,

$\\{0,8,36,96,228\\}$, $\\{0,35,98,141,203\\}$, $\\{0,21,53,155,179\\}$,

$\\{0,20,127,222,315\\}$, $\\{0,25,162,243,323\\}$, $\\{0,14,190,229,322\\}$,

$\\{0,30,87,146,310\\}$, $\\{0,18,131,242,297\\}$, $\\{0,26,198,235,285\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}276)$ for $x<276$,
$x\mapsto(x-276+4j~{}(\mathrm{mod}~{}48))+276$ for $x\geq 276$, $0\leq j<276$.
[(324, ((18, 276, ((276, 1), (48, 4)))), ((12, 23), (48, 1)))]

$12^{23}68^{1}$ With the point set $\\{0,1,\dots,343\\}$ partitioned into
residue classes modulo $23$ for $\\{0,1,\dots,275\\}$, and
$\\{276,277,\dots,343\\}$, the design is generated from

$\\{60,341,75,237,178\\}$, $\\{17,239,64,15,307\\}$, $\\{173,85,6,216,224\\}$,

$\\{87,55,116,52,282\\}$, $\\{213,269,90,299,188\\}$,
$\\{275,61,303,185,255\\}$,

$\\{318,259,265,191,165\\}$, $\\{233,342,147,106,252\\}$,
$\\{161,248,241,325,76\\}$,

$\\{306,43,197,119,64\\}$, $\\{0,5,22,147,318\\}$, $\\{0,4,57,164,317\\}$,

$\\{0,12,48,108,132\\}$, $\\{0,1,34,45,72\\}$, $\\{0,14,135,248,290\\}$,

$\\{0,30,95,170,325\\}$, $\\{0,10,193,209,289\\}$, $\\{0,13,63,102,309\\}$,

$\\{0,18,166,203,296\\}$, $\\{0,9,40,159,276\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}276)$ for $x<276$,
$x\mapsto(x-276+5j~{}(\mathrm{mod}~{}60))+276$ for $276\leq x<336$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}8))+336$ for $x\geq 336$, $0\leq j<276$.
[(344, ((20, 276, ((276, 1), (60, 5), (8, 2)))), ((12, 23), (68, 1)))]

$12^{24}32^{1}$ With the point set $\\{0,1,\dots,319\\}$ partitioned into
residue classes modulo $24$ for $\\{0,1,\dots,287\\}$, and
$\\{288,289,\dots,319\\}$, the design is generated from

$\\{309,261,170,111,185\\}$, $\\{188,317,11,222,221\\}$,
$\\{300,266,61,245,127\\}$,

$\\{107,127,135,240,296\\}$, $\\{266,51,319,217,92\\}$,
$\\{36,166,285,196,1\\}$,

$\\{27,307,137,49,245\\}$, $\\{210,48,111,108,95\\}$,
$\\{120,146,65,151,134\\}$,

$\\{0,2,54,252,303\\}$, $\\{0,9,94,176,308\\}$, $\\{0,6,50,137,232\\}$,

$\\{0,10,42,67,223\\}$, $\\{0,19,80,103,148\\}$, $\\{0,11,51,109,152\\}$,

$\\{0,18,97,134,161\\}$, $\\{0,7,53,124,153\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}288)$ for $x<288$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}24))+288$ for $288\leq x<312$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+312$ for $x\geq 312$, $0\leq j<288$.
[(320, ((17, 288, ((288, 1), (24, 1), (8, 1)))), ((12, 24), (32, 1)))]

$12^{24}52^{1}$ With the point set $\\{0,1,\dots,339\\}$ partitioned into
residue classes modulo $24$ for $\\{0,1,\dots,287\\}$, and
$\\{288,289,\dots,339\\}$, the design is generated from

$\\{110,286,312,184,33\\}$, $\\{87,174,240,31,307\\}$,
$\\{76,299,67,61,174\\}$,

$\\{68,335,222,191,70\\}$, $\\{96,5,165,135,51\\}$, $\\{56,111,75,197,2\\}$,

$\\{331,173,120,190,172\\}$, $\\{330,2,270,227,277\\}$,
$\\{74,223,174,300,182\\}$,

$\\{113,314,54,139,136\\}$, $\\{0,34,140,228,326\\}$, $\\{0,22,47,193,336\\}$,

$\\{0,12,28,104,185\\}$, $\\{0,4,44,163,227\\}$, $\\{0,14,71,138,170\\}$,

$\\{0,29,162,220,309\\}$, $\\{0,11,62,89,172\\}$, $\\{0,10,187,208,299\\}$,

$\\{0,5,38,251,300\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}288)$ for $x<288$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}32))+288$ for $288\leq x<320$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+320$ for $320\leq x<336$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+336$ for $x\geq 336$, $0\leq j<288$.
[(340, ((19, 288, ((288, 1), (32, 1), (16, 1), (4, 1)))), ((12, 24), (52,
1)))]

$12^{27}4^{1}$ With the point set $\\{0,1,\dots,327\\}$ partitioned into
residue classes modulo $27$ for $\\{0,1,\dots,323\\}$, and
$\\{324,325,326,327\\}$, the design is generated from

$\\{210,26,110,200,214\\}$, $\\{264,306,71,322,209\\}$,
$\\{189,225,33,259,113\\}$,

$\\{128,192,210,203,255\\}$, $\\{169,109,160,261,286\\}$,
$\\{138,36,19,158,13\\}$,

$\\{144,39,26,72,313\\}$, $\\{0,3,94,137,161\\}$, $\\{0,1,30,259,324\\}$,

$\\{0,15,86,215,246\\}$, $\\{0,12,44,203,225\\}$, $\\{0,5,53,115,176\\}$,

$\\{0,8,47,204,283\\}$, $\\{0,2,28,87,144\\}$, $\\{0,35,103,141,210\\}$,

$\\{0,19,40,96,170\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}324)$ for $x<324$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+324$ for $x\geq 324$, $0\leq j<324$.
[(328, ((16, 324, ((324, 1), (4, 1)))), ((12, 27), (4, 1)))]

$13^{8}17^{1}$ With the point set $\\{0,1,\dots,120\\}$ partitioned into
residue classes modulo $8$ for $\\{0,1,\dots,103\\}$, and
$\\{104,105,\dots,120\\}$, the design is generated from

$\\{19,108,60,61,7\\}$, $\\{0,2,19,100,112\\}$, $\\{0,7,29,44,105\\}$,

$\\{0,3,28,33,46\\}$, $\\{0,10,31,45,65\\}$, $\\{0,9,36,47,117\\}$,

$\\{0,26,52,78,120\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}104)$ for $x<104$,
$x\mapsto(x-104+2j~{}(\mathrm{mod}~{}16))+104$ for $104\leq x<120$,
$120\mapsto 120$, $0\leq j<104$ for the first six blocks, $0\leq j<26$ for the
last block.
[(121, ((6, 104, ((104, 1), (16, 2), (1, 1))), (1, 26, ((104, 1), (16, 2), (1,
1)))), ((13, 8), (17, 1)))]

$13^{12}1^{1}$ With the point set $\\{0,1,\dots,156\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,155\\}$, and $\\{156\\}$, the
design is generated from

$\\{79,33,38,29,142\\}$, $\\{21,108,41,133,102\\}$, $\\{0,2,10,29,32\\}$,

$\\{0,1,14,54,71\\}$, $\\{0,11,37,88,111\\}$, $\\{0,7,28,66,101\\}$,

$\\{0,15,33,49,91\\}$, $\\{0,39,78,117,156\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$, $156\mapsto
156$, $0\leq j<156$ for the first seven blocks, $0\leq j<39$ for the last
block.
[(157, ((7, 156, ((156, 1), (1, 1))), (1, 39, ((156, 1), (1, 1)))), ((13, 12),
(1, 1)))]

$13^{12}21^{1}$ With the point set $\\{0,1,\dots,176\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,176\\}$, the design is generated from

$\\{124,152,156,101,21\\}$, $\\{47,85,147,28,21\\}$, $\\{0,1,3,146,169\\}$,

$\\{0,5,22,63,168\\}$, $\\{0,21,65,107,167\\}$, $\\{0,8,55,124,161\\}$,

$\\{0,6,33,67,85\\}$, $\\{0,4,20,35,110\\}$, $\\{0,9,54,83,97\\}$,

$\\{0,39,78,117,176\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}12))+156$ for $156\leq x<168$,
$x\mapsto(x+2j~{}(\mathrm{mod}~{}8))+168$ for $168\leq x<176$, $176\mapsto
176$, $0\leq j<156$ for the first nine blocks, $0\leq j<39$ for the last
block.
[(177, ((9, 156, ((156, 1), (12, 1), (8, 2), (1, 1))), (1, 39, ((156, 1), (12,
1), (8, 2), (1, 1)))), ((13, 12), (21, 1)))]

$13^{12}41^{1}$ With the point set $\\{0,1,\dots,196\\}$ partitioned into
residue classes modulo $12$ for $\\{0,1,\dots,155\\}$, and
$\\{156,157,\dots,196\\}$, the design is generated from

$\\{166,115,111,47,93\\}$, $\\{76,185,66,75,47\\}$, $\\{107,27,163,0,65\\}$,

$\\{114,32,168,17,19\\}$, $\\{0,3,8,102,160\\}$, $\\{0,7,21,126,192\\}$,

$\\{0,26,71,112,168\\}$, $\\{0,6,40,109,177\\}$, $\\{0,23,75,100,191\\}$,

$\\{0,16,33,83,161\\}$, $\\{0,11,31,66,124\\}$, $\\{0,39,78,117,196\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}156)$ for $x<156$,
$x\mapsto(x-156+3j~{}(\mathrm{mod}~{}36))+156$ for $156\leq x<192$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+192$ for $192\leq x<196$, $196\mapsto
196$, $0\leq j<156$ for the first 11 blocks, $0\leq j<39$ for the last block.
[(197, ((11, 156, ((156, 1), (36, 3), (4, 1), (1, 1))), (1, 39, ((156, 1),
(36, 3), (4, 1), (1, 1)))), ((13, 12), (41, 1)))]

$13^{16}5^{1}$ With the point set $\\{0,1,\dots,212\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,207\\}$, and
$\\{208,209,210,211,212\\}$, the design is generated from

$\\{92,58,2,45,89\\}$, $\\{188,103,115,104,85\\}$, $\\{82,72,0,107,14\\}$,

$\\{0,2,8,127,193\\}$, $\\{0,7,46,141,208\\}$, $\\{0,28,57,120,157\\}$,

$\\{0,21,59,99,153\\}$, $\\{0,20,62,137,159\\}$, $\\{0,24,50,77,110\\}$,

$\\{0,4,9,45,147\\}$, $\\{0,52,104,156,212\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}208)$ for $x<208$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+208$ for $208\leq x<212$, $212\mapsto
212$, $0\leq j<208$ for the first ten blocks, $0\leq j<52$ for the last block.
[(213, ((10, 208, ((208, 1), (4, 1), (1, 1))), (1, 52, ((208, 1), (4, 1), (1,
1)))), ((13, 16), (5, 1)))]

$13^{16}25^{1}$ With the point set $\\{0,1,\dots,232\\}$ partitioned into
residue classes modulo $16$ for $\\{0,1,\dots,207\\}$, and
$\\{208,209,\dots,232\\}$, the design is generated from

$\\{207,123,149,124,212\\}$, $\\{138,91,115,28,120\\}$,
$\\{217,62,31,204,53\\}$,

$\\{6,39,88,178,193\\}$, $\\{0,2,67,73,217\\}$, $\\{0,3,122,132,218\\}$,

$\\{0,4,12,127,170\\}$, $\\{0,13,53,130,147\\}$, $\\{0,7,34,62,106\\}$,

$\\{0,19,39,107,152\\}$, $\\{0,14,51,162,219\\}$, $\\{0,11,41,149,231\\}$,

$\\{0,52,104,156,232\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}208)$ for $x<208$,
$x\mapsto(x-208+3j~{}(\mathrm{mod}~{}24))+208$ for $208\leq x<232$,
$232\mapsto 232$, $0\leq j<208$ for the first 12 blocks, $0\leq j<52$ for the
last block.
[(233, ((12, 208, ((208, 1), (24, 3), (1, 1))), (1, 52, ((208, 1), (24, 3),
(1, 1)))), ((13, 16), (25, 1)))]

$13^{20}1^{1}$ With the point set $\\{0,1,\dots,260\\}$ partitioned into
residue classes modulo $20$ for $\\{0,1,\dots,259\\}$, and $\\{260\\}$, the
design is generated from

$\\{132,30,37,91,158\\}$, $\\{150,95,129,47,125\\}$,
$\\{208,65,144,100,159\\}$,

$\\{255,238,167,0,124\\}$, $\\{206,144,88,125,195\\}$, $\\{0,2,68,86,99\\}$,

$\\{0,12,57,110,149\\}$, $\\{0,1,9,134,184\\}$, $\\{0,3,27,90,191\\}$,

$\\{0,14,47,89,105\\}$, $\\{0,6,29,112,144\\}$, $\\{0,10,38,151,224\\}$,

$\\{0,65,130,195,260\\}$, $\\{0,52,104,156,208\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}260)$ for $x<260$, $260\mapsto
260$, $0\leq j<260$ for the first 12 blocks, $0\leq j<65$ for the next block,
$0\leq j<52$ for the last block.
[(261, ((12, 260, ((260, 1), (1, 1))), (1, 65, ((260, 1), (1, 1))), (1, 52,
((260, 1), (1, 1)))), ((13, 20), (1, 1)))]

$14^{8}6^{1}$ With the point set $\\{0,1,\dots,117\\}$ partitioned into
residue classes modulo $8$ for $\\{0,1,\dots,111\\}$, and
$\\{112,113,\dots,117\\}$, the design is generated from

$\\{55,82,62,73,114\\}$, $\\{30,64,83,1,109\\}$, $\\{106,65,53,75,76\\}$,

$\\{0,1,47,108,112\\}$, $\\{0,2,65,100,109\\}$, $\\{0,7,58,76,91\\}$,

$\\{0,21,35,55,97\\}$, $\\{0,3,22,28,74\\}$, $\\{0,13,50,67,73\\}$,

$\\{0,25,42,68,99\\}$, $\\{0,10,37,39,116\\}$

by the mapping: $x\mapsto x+2j~{}(\mathrm{mod}~{}112)$ for $x<112$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+112$ for $112\leq x<116$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}2))+116$ for $x\geq 116$, $0\leq j<56$.
[(118, ((11, 56, ((112, 2), (4, 1), (2, 1)))), ((14, 8), (6, 1)))]

$16^{6}20^{1}$ With the point set $\\{0,1,\dots,115\\}$ partitioned into
residue classes modulo $6$ for $\\{0,1,\dots,95\\}$, and
$\\{96,97,\dots,115\\}$, the design is generated from

$\\{0,1,3,10,112\\}$, $\\{0,4,32,47,63\\}$, $\\{0,20,46,75,96\\}$,

$\\{0,11,34,51,106\\}$, $\\{0,14,39,58,107\\}$, $\\{0,5,13,74,99\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}96)$ for $x<96$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+96$ for $96\leq x<112$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+112$ for $x\geq 112$, $0\leq j<96$.
[(116, ((6, 96, ((96, 1), (16, 1), (4, 1)))), ((16, 6), (20, 1)))]

$16^{7}12^{1}$ With the point set $\\{0,1,\dots,123\\}$ partitioned into
residue classes modulo $7$ for $\\{0,1,\dots,111\\}$, and
$\\{112,113,\dots,123\\}$, the design is generated from

$\\{0,1,3,102,112\\}$, $\\{0,5,23,90,114\\}$, $\\{0,9,46,71,113\\}$,

$\\{0,15,34,72,88\\}$, $\\{0,4,30,36,83\\}$, $\\{0,8,20,51,68\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}112)$ for $x<112$,
$x\mapsto(x-112+3j~{}(\mathrm{mod}~{}12))+112$ for $x\geq 112$, $0\leq j<112$.
[(124, ((6, 112, ((112, 1), (12, 3)))), ((16, 7), (12, 1)))]

$16^{8}4^{1}$ With the point set $\\{0,1,\dots,131\\}$ partitioned into
residue classes modulo $8$ for $\\{0,1,\dots,127\\}$, and
$\\{128,129,130,131\\}$, the design is generated from

$\\{0,1,3,122,128\\}$, $\\{0,4,41,46,61\\}$, $\\{0,12,31,59,89\\}$,

$\\{0,10,27,53,105\\}$, $\\{0,13,35,49,103\\}$, $\\{0,11,29,73,94\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}128)$ for $x<128$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+128$ for $x\geq 128$, $0\leq j<128$.
[(132, ((6, 128, ((128, 1), (4, 1)))), ((16, 8), (4, 1)))]

$16^{9}36^{1}$ With the point set $\\{0,1,\dots,179\\}$ partitioned into
residue classes modulo $9$ for $\\{0,1,\dots,143\\}$, and
$\\{144,145,\dots,179\\}$, the design is generated from

$\\{99,111,164,13,125\\}$, $\\{159,109,47,96,30\\}$,
$\\{106,135,2,102,151\\}$,

$\\{0,1,3,123,169\\}$, $\\{0,5,39,64,74\\}$, $\\{0,6,48,103,150\\}$,

$\\{0,8,28,101,170\\}$, $\\{0,19,57,113,164\\}$, $\\{0,15,67,83,167\\}$,

$\\{0,7,91,114,146\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}36))+144$ for $x\geq 144$, $0\leq j<144$.
[(180, ((10, 144, ((144, 1), (36, 1)))), ((16, 9), (36, 1)))]

$16^{10}8^{1}$ With the point set $\\{0,1,\dots,167\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,167\\}$, the design is generated from

$\\{27,82,164,94,28\\}$, $\\{49,117,21,150,32\\}$, $\\{0,2,38,41,165\\}$,

$\\{0,7,63,72,86\\}$, $\\{0,15,34,61,77\\}$, $\\{0,4,25,51,73\\}$,

$\\{0,6,24,82,131\\}$, $\\{0,5,13,57,128\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+160$ for $x\geq 160$, $0\leq j<160$.
[(168, ((8, 160, ((160, 1), (8, 1)))), ((16, 10), (8, 1)))]

$16^{10}20^{1}$ With the point set $\\{0,1,\dots,179\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,179\\}$, the design is generated from

$\\{142,16,95,88,124\\}$, $\\{139,154,174,22,81\\}$, $\\{0,1,3,26,155\\}$,

$\\{0,4,16,93,107\\}$, $\\{0,21,45,82,168\\}$, $\\{0,17,56,122,161\\}$,

$\\{0,9,51,84,95\\}$, $\\{0,13,48,111,162\\}$, $\\{0,19,46,138,176\\}$,

$\\{0,32,64,96,128\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}20))+160$ for $x\geq 160$, $0\leq j<160$ for
the first nine blocks, $0\leq j<32$ for the last block.
[(180, ((9, 160, ((160, 1), (20, 1))), (1, 32, ((160, 1), (20, 1)))), ((16,
10), (20, 1)))]

$16^{10}28^{1}$ With the point set $\\{0,1,\dots,187\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,187\\}$, the design is generated from

$\\{37,32,74,73,177\\}$, $\\{17,10,118,165,91\\}$, $\\{153,182,100,155,88\\}$,

$\\{0,3,9,22,184\\}$, $\\{0,4,29,116,132\\}$, $\\{0,11,26,88,122\\}$,

$\\{0,8,54,117,168\\}$, $\\{0,18,94,139,167\\}$, $\\{0,14,31,89,113\\}$,

$\\{0,23,92,127,173\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+160$ for $160\leq x<176$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}8))+176$ for $176\leq x<184$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}4))+184$ for $x\geq 184$, $0\leq j<160$.
[(188, ((10, 160, ((160, 1), (16, 1), (8, 1), (4, 1)))), ((16, 10), (28, 1)))]

$16^{10}36^{1}$ With the point set $\\{0,1,\dots,195\\}$ partitioned into
residue classes modulo $9$ for $\\{0,1,\dots,143\\}$,
$\\{144,145,\dots,159\\}$, and $\\{160,161,\dots,195\\}$, the design is
generated from

$\\{157,125,56,57,160\\}$, $\\{133,110,172,40,99\\}$, $\\{6,128,46,192,14\\}$,

$\\{5,129,11,151,63\\}$, $\\{0,2,5,147,164\\}$, $\\{0,12,106,153,185\\}$,

$\\{0,13,28,151,161\\}$, $\\{0,24,65,107,189\\}$, $\\{0,14,109,125,194\\}$,

$\\{0,10,31,98,115\\}$, $\\{0,7,55,80,174\\}$, $\\{0,4,57,101,192\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}144)$ for $x<144$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}16))+144$ for $144\leq x<160$,
$x\mapsto(x-160+j~{}(\mathrm{mod}~{}36))+160$ for $x\geq 160$, $0\leq j<144$.
[(196, ((12, 144, ((144, 1), (16, 1), (36, 1)))), ((16, 9), (16, 1), (36,
1)))]

$16^{10}40^{1}$ With the point set $\\{0,1,\dots,199\\}$ partitioned into
residue classes modulo $10$ for $\\{0,1,\dots,159\\}$, and
$\\{160,161,\dots,199\\}$, the design is generated from

$\\{181,39,90,12,27\\}$, $\\{116,85,83,121,37\\}$, $\\{111,140,83,36,194\\}$,

$\\{27,101,76,197,10\\}$, $\\{0,1,4,138,196\\}$, $\\{0,14,67,139,164\\}$,

$\\{0,6,45,89,189\\}$, $\\{0,13,37,55,172\\}$, $\\{0,9,101,117,162\\}$,

$\\{0,8,62,149,168\\}$, $\\{0,7,65,126,173\\}$, $\\{0,32,64,96,128\\}$

by the mapping: $x\mapsto x+j~{}(\mathrm{mod}~{}160)$ for $x<160$,
$x\mapsto(x+j~{}(\mathrm{mod}~{}40))+160$ for $x\geq 160$, $0\leq j<160$ for
the first 11 blocks, $0\leq j<32$ for the last block.