Best Known (3, 18, s)-Nets in Base 64
(3, 18, 104)-Net over F64 — Constructive and digital
Digital (3, 18, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
(3, 18, 113)-Net over F64 — Digital
Digital (3, 18, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
(3, 18, 129)-Net in Base 64 — Constructive
(3, 18, 129)-net in base 64, using
- 3 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 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, 18, 129)-net over F128, using
(3, 18, 1303)-Net in Base 64 — Upper bound on s
There is no (3, 18, 1304)-net in base 64, because
- 1 times m-reduction [i] would yield (3, 17, 1304)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 5 094912 080641 797161 001078 070555 > 6417 [i]