Best Known (18, 69, s)-Nets in Base 64
(18, 69, 177)-Net over F64 — Constructive and digital
Digital (18, 69, 177)-net over F64, using
- t-expansion [i] based on digital (7, 69, 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
(18, 69, 257)-Net in Base 64 — Constructive
(18, 69, 257)-net in base 64, using
- 3 times m-reduction [i] based on (18, 72, 257)-net in base 64, using
- base change [i] based on digital (0, 54, 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, 54, 257)-net over F256, using
(18, 69, 281)-Net over F64 — Digital
Digital (18, 69, 281)-net over F64, using
- net from sequence [i] based on digital (18, 280)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 18 and N(F) ≥ 281, using
(18, 69, 13203)-Net in Base 64 — Upper bound on s
There is no (18, 69, 13204)-net in base 64, because
- 1 times m-reduction [i] would yield (18, 68, 13204)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 661 748384 899780 240179 764874 306959 537719 629686 944294 973081 144976 536889 384950 753806 196884 883775 590230 943924 589299 248585 756528 > 6468 [i]