Best Known (10, 39, s)-Nets in Base 64
(10, 39, 177)-Net over F64 — Constructive and digital
Digital (10, 39, 177)-net over F64, using
- t-expansion [i] based on digital (7, 39, 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
(10, 39, 225)-Net over F64 — Digital
Digital (10, 39, 225)-net over F64, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
(10, 39, 257)-Net in Base 64 — Constructive
(10, 39, 257)-net in base 64, using
- 1 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- base change [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
(10, 39, 7659)-Net in Base 64 — Upper bound on s
There is no (10, 39, 7660)-net in base 64, because
- 1 times m-reduction [i] would yield (10, 38, 7660)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 431 414308 460318 993035 844473 205637 046456 784483 934919 072892 224199 442520 > 6438 [i]