Best Known (67−46, 67, s)-Nets in Base 64
(67−46, 67, 177)-Net over F64 — Constructive and digital
Digital (21, 67, 177)-net over F64, using
- t-expansion [i] based on digital (7, 67, 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
(67−46, 67, 288)-Net in Base 64 — Constructive
(21, 67, 288)-net in base 64, using
- 17 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
(67−46, 67, 342)-Net over F64 — Digital
Digital (21, 67, 342)-net over F64, using
- t-expansion [i] based on digital (20, 67, 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
(67−46, 67, 27315)-Net in Base 64 — Upper bound on s
There is no (21, 67, 27316)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 10 329666 782401 849014 266056 977084 093326 637995 454130 775506 038463 809350 606582 203946 608335 738974 028911 193559 175509 683054 130216 > 6467 [i]