Best Known (34−25, 34, s)-Nets in Base 64
(34−25, 34, 177)-Net over F64 — Constructive and digital
Digital (9, 34, 177)-net over F64, using
- t-expansion [i] based on digital (7, 34, 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
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(34−25, 34, 209)-Net over F64 — Digital
Digital (9, 34, 209)-net over F64, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
(34−25, 34, 257)-Net in Base 64 — Constructive
(9, 34, 257)-net in base 64, using
- 2 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on digital (0, 27, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 27, 257)-net over F256, using
(34−25, 34, 7774)-Net in Base 64 — Upper bound on s
There is no (9, 34, 7775)-net in base 64, because
- 1 times m-reduction [i] would yield (9, 33, 7775)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 401759 997469 005727 005075 852471 865505 384439 804867 696814 484641 > 6433 [i]