Best Known (23−16, 23, s)-Nets in Base 64
(23−16, 23, 177)-Net over F64 — Constructive and digital
Digital (7, 23, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
(23−16, 23, 258)-Net in Base 64 — Constructive
(7, 23, 258)-net in base 64, using
- 1 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
- base change [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 18, 258)-net over F256, using
(23−16, 23, 289)-Net in Base 64
(7, 23, 289)-net in base 64, using
- 1 times m-reduction [i] based on (7, 24, 289)-net in base 64, using
- base change [i] based on digital (1, 18, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 18, 289)-net over F256, using
(23−16, 23, 9309)-Net in Base 64 — Upper bound on s
There is no (7, 23, 9310)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 348461 234339 679391 053162 786156 884410 699897 > 6423 [i]