Best Known (78−58, 78, s)-Nets in Base 64
(78−58, 78, 177)-Net over F64 — Constructive and digital
Digital (20, 78, 177)-net over F64, using
- t-expansion [i] based on digital (7, 78, 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
(78−58, 78, 257)-Net in Base 64 — Constructive
(20, 78, 257)-net in base 64, using
- 2 times m-reduction [i] based on (20, 80, 257)-net in base 64, using
- base change [i] based on digital (0, 60, 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, 60, 257)-net over F256, using
(78−58, 78, 342)-Net over F64 — Digital
Digital (20, 78, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(78−58, 78, 13344)-Net in Base 64 — Upper bound on s
There is no (20, 78, 13345)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 452331 370351 593014 381215 423092 192828 303818 138859 418893 263695 048653 256688 286335 008519 944745 578093 332492 863013 389618 561805 757800 478129 919648 > 6478 [i]