Best Known (47−37, 47, s)-Nets in Base 64
(47−37, 47, 177)-Net over F64 — Constructive and digital
Digital (10, 47, 177)-net over F64, using
- t-expansion [i] based on digital (7, 47, 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
(47−37, 47, 192)-Net in Base 64 — Constructive
(10, 47, 192)-net in base 64, using
- 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
(47−37, 47, 225)-Net over F64 — Digital
Digital (10, 47, 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
(47−37, 47, 4940)-Net in Base 64 — Upper bound on s
There is no (10, 47, 4941)-net in base 64, because
- 1 times m-reduction [i] would yield (10, 46, 4941)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 121433 622767 692213 455237 245529 832548 009685 281776 610353 741598 542936 027405 876914 303048 > 6446 [i]