Best Known (37−31, 37, s)-Nets in Base 64
(37−31, 37, 128)-Net over F64 — Constructive and digital
Digital (6, 37, 128)-net over F64, using
- t-expansion [i] based on digital (5, 37, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(37−31, 37, 129)-Net in Base 64 — Constructive
(6, 37, 129)-net in base 64, using
- 5 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
- base change [i] based on digital (0, 36, 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, 36, 129)-net over F128, using
(37−31, 37, 161)-Net over F64 — Digital
Digital (6, 37, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
(37−31, 37, 2197)-Net in Base 64 — Upper bound on s
There is no (6, 37, 2198)-net in base 64, because
- 1 times m-reduction [i] would yield (6, 36, 2198)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 106029 364502 907677 541900 531019 074690 362667 435377 621715 262914 147016 > 6436 [i]