Best Known (32, 32+39, s)-Nets in Base 64
(32, 32+39, 513)-Net over F64 — Constructive and digital
Digital (32, 71, 513)-net over F64, using
- t-expansion [i] based on digital (28, 71, 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
(32, 32+39, 585)-Net over F64 — Digital
Digital (32, 71, 585)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6471, 585, F64, 39) (dual of [585, 514, 40]-code), using
- 68 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 17 times 0, 1, 47 times 0) [i] based on linear OA(6467, 513, F64, 39) (dual of [513, 446, 40]-code), using
- extended algebraic-geometric code AGe(F,473P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- extended algebraic-geometric code AGe(F,473P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- 68 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 17 times 0, 1, 47 times 0) [i] based on linear OA(6467, 513, F64, 39) (dual of [513, 446, 40]-code), using
(32, 32+39, 567825)-Net in Base 64 — Upper bound on s
There is no (32, 71, 567826)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 70, 567826)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 2 707704 087205 317099 063829 164915 825642 666570 701264 443704 497106 440635 085827 923826 475192 090188 349895 278504 281238 600166 645544 447744 > 6470 [i]