Best Known (32, 91, s)-Nets in Base 64
(32, 91, 513)-Net over F64 — Constructive and digital
Digital (32, 91, 513)-net over F64, using
- t-expansion [i] based on digital (28, 91, 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, 91, 74659)-Net in Base 64 — Upper bound on s
There is no (32, 91, 74660)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 90, 74660)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 600208 931560 093735 361796 034586 466552 673474 916926 564870 989118 267274 070098 608509 372663 795872 212395 631974 239792 772621 998335 410053 580939 415038 492725 071271 113766 088232 > 6490 [i]