Best Known (16, 16+30, s)-Nets in Base 64
(16, 16+30, 177)-Net over F64 — Constructive and digital
Digital (16, 46, 177)-net over F64, using
- t-expansion [i] based on digital (7, 46, 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
(16, 16+30, 267)-Net over F64 — Digital
Digital (16, 46, 267)-net over F64, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 16 and N(F) ≥ 267, using
(16, 16+30, 288)-Net in Base 64 — Constructive
(16, 46, 288)-net in base 64, using
- 3 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 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, 42, 288)-net over F128, using
(16, 16+30, 321)-Net in Base 64
(16, 46, 321)-net in base 64, using
- 10 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 42, 321)-net over F256, using
(16, 16+30, 35260)-Net in Base 64 — Upper bound on s
There is no (16, 46, 35261)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 121440 915791 282277 410110 854331 016468 019387 816655 595938 835893 833357 312555 999878 139760 > 6446 [i]