Best Known (20−15, 20, s)-Nets in Base 64
(20−15, 20, 128)-Net over F64 — Constructive and digital
Digital (5, 20, 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
(20−15, 20, 133)-Net over F64 — Digital
Digital (5, 20, 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
(20−15, 20, 257)-Net in Base 64 — Constructive
(5, 20, 257)-net in base 64, using
- base change [i] based on digital (0, 15, 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
(20−15, 20, 4283)-Net in Base 64 — Upper bound on s
There is no (5, 20, 4284)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 19, 4284)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 20802 048243 752227 803994 467471 393370 > 6419 [i]