Best Known (64−41, 64, s)-Nets in Base 64
(64−41, 64, 177)-Net over F64 — Constructive and digital
Digital (23, 64, 177)-net over F64, using
- t-expansion [i] based on digital (7, 64, 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
(64−41, 64, 288)-Net in Base 64 — Constructive
(23, 64, 288)-net in base 64, using
- t-expansion [i] based on (22, 64, 288)-net in base 64, using
- 27 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 27 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(64−41, 64, 342)-Net over F64 — Digital
Digital (23, 64, 342)-net over F64, using
- t-expansion [i] based on digital (20, 64, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(64−41, 64, 64471)-Net in Base 64 — Upper bound on s
There is no (23, 64, 64472)-net in base 64, because
- 1 times m-reduction [i] would yield (23, 63, 64472)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 615788 717782 710777 947725 394856 836745 562275 438096 913526 145893 738001 510290 128920 391272 887144 546740 951784 490306 367351 > 6463 [i]