Best Known (55, 96, s)-Nets in Base 32
(55, 96, 294)-Net over F32 — Constructive and digital
Digital (55, 96, 294)-net over F32, using
- 321 times duplication [i] based on digital (54, 95, 294)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 20, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 27, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 48, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 20, 98)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(55, 96, 513)-Net in Base 32 — Constructive
(55, 96, 513)-net in base 32, using
- t-expansion [i] based on (46, 96, 513)-net in base 32, using
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(55, 96, 2104)-Net over F32 — Digital
Digital (55, 96, 2104)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3296, 2104, F32, 41) (dual of [2104, 2008, 42]-code), using
- 2007 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 24 times 0, 1, 26 times 0, 1, 28 times 0, 1, 32 times 0, 1, 34 times 0, 1, 38 times 0, 1, 41 times 0, 1, 45 times 0, 1, 50 times 0, 1, 54 times 0, 1, 59 times 0, 1, 64 times 0, 1, 71 times 0, 1, 77 times 0, 1, 85 times 0, 1, 92 times 0, 1, 101 times 0, 1, 110 times 0, 1, 120 times 0, 1, 132 times 0, 1, 143 times 0, 1, 157 times 0, 1, 171 times 0) [i] based on linear OA(3241, 42, F32, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,32)), using
- dual of repetition code with length 42 [i]
- 2007 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 24 times 0, 1, 26 times 0, 1, 28 times 0, 1, 32 times 0, 1, 34 times 0, 1, 38 times 0, 1, 41 times 0, 1, 45 times 0, 1, 50 times 0, 1, 54 times 0, 1, 59 times 0, 1, 64 times 0, 1, 71 times 0, 1, 77 times 0, 1, 85 times 0, 1, 92 times 0, 1, 101 times 0, 1, 110 times 0, 1, 120 times 0, 1, 132 times 0, 1, 143 times 0, 1, 157 times 0, 1, 171 times 0) [i] based on linear OA(3241, 42, F32, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,32)), using
(55, 96, 3779251)-Net in Base 32 — Upper bound on s
There is no (55, 96, 3779252)-net in base 32, because
- 1 times m-reduction [i] would yield (55, 95, 3779252)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 97555 016800 533993 079435 306240 403866 600861 178777 039716 216725 117672 759793 420207 080309 233337 131206 192681 945685 239640 223439 501892 973991 539455 383736 > 3295 [i]