Best Known (1, 5, s)-Nets in Base 64
(1, 5, 80)-Net over F64 — Constructive and digital
Digital (1, 5, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
(1, 5, 81)-Net over F64 — Digital
Digital (1, 5, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
(1, 5, 129)-Net in Base 64 — Constructive
(1, 5, 129)-net in base 64, using
- 2 times m-reduction [i] based on (1, 7, 129)-net in base 64, using
- base change [i] based on digital (0, 6, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 6, 129)-net over F128, using
(1, 5, 735)-Net in Base 64 — Upper bound on s
There is no (1, 5, 736)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 1076 549041 > 645 [i]