Best Known (56−42, 56, s)-Nets in Base 64
(56−42, 56, 177)-Net over F64 — Constructive and digital
Digital (14, 56, 177)-net over F64, using
- t-expansion [i] based on digital (7, 56, 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
(56−42, 56, 257)-Net in Base 64 — Constructive
(14, 56, 257)-net in base 64, using
- base change [i] based on digital (0, 42, 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
(56−42, 56, 257)-Net over F64 — Digital
Digital (14, 56, 257)-net over F64, using
- t-expansion [i] based on digital (12, 56, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
(56−42, 56, 9018)-Net in Base 64 — Upper bound on s
There is no (14, 56, 9019)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 140144 030813 302905 064191 453174 529400 705483 655953 381654 083338 449331 809781 861900 343896 899517 446966 456932 > 6456 [i]