Best Known (30−25, 30, s)-Nets in Base 64
(30−25, 30, 128)-Net over F64 — Constructive and digital
Digital (5, 30, 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
(30−25, 30, 129)-Net in Base 64 — Constructive
(5, 30, 129)-net in base 64, using
- 5 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 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, 30, 129)-net over F128, using
(30−25, 30, 133)-Net over F64 — Digital
Digital (5, 30, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(30−25, 30, 1939)-Net in Base 64 — Upper bound on s
There is no (5, 30, 1940)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 29, 1940)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 24022 876117 911553 677578 301175 103915 971018 270775 532148 > 6429 [i]