Best Known (16, 16+32, s)-Nets in Base 64
(16, 16+32, 177)-Net over F64 — Constructive and digital
Digital (16, 48, 177)-net over F64, using
- t-expansion [i] based on digital (7, 48, 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+32, 267)-Net over F64 — Digital
Digital (16, 48, 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+32, 288)-Net in Base 64 — Constructive
(16, 48, 288)-net in base 64, using
- 1 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+32, 321)-Net in Base 64
(16, 48, 321)-net in base 64, using
- 8 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+32, 28289)-Net in Base 64 — Upper bound on s
There is no (16, 48, 28290)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 497 577289 428907 042030 844804 243960 461288 656859 914364 959393 097720 866118 182433 507105 159960 > 6448 [i]