Best Known (9, 9+33, s)-Nets in Base 64
(9, 9+33, 177)-Net over F64 — Constructive and digital
Digital (9, 42, 177)-net over F64, using
- t-expansion [i] based on digital (7, 42, 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
(9, 9+33, 192)-Net in Base 64 — Constructive
(9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 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
(9, 9+33, 209)-Net over F64 — Digital
Digital (9, 42, 209)-net over F64, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
(9, 9+33, 4579)-Net in Base 64 — Upper bound on s
There is no (9, 42, 4580)-net in base 64, because
- 1 times m-reduction [i] would yield (9, 41, 4580)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 113 351419 761259 404746 566911 308790 948679 401202 345924 906284 528846 155847 149434 > 6441 [i]