Best Known (56−38, 56, s)-Nets in Base 64
(56−38, 56, 177)-Net over F64 — Constructive and digital
Digital (18, 56, 177)-net over F64, using
- t-expansion [i] based on digital (7, 56, 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
(56−38, 56, 281)-Net over F64 — Digital
Digital (18, 56, 281)-net over F64, using
- net from sequence [i] based on digital (18, 280)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 18 and N(F) ≥ 281, using
(56−38, 56, 288)-Net in Base 64 — Constructive
(18, 56, 288)-net in base 64, using
- 7 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
(56−38, 56, 321)-Net in Base 64
(18, 56, 321)-net in base 64, using
- 8 times m-reduction [i] based on (18, 64, 321)-net in base 64, using
- base change [i] based on digital (2, 48, 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, 48, 321)-net over F256, using
(56−38, 56, 26497)-Net in Base 64 — Upper bound on s
There is no (18, 56, 26498)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 140062 049400 561604 265733 062289 992257 481673 667093 133038 472214 361936 548421 111348 260967 843917 376319 400256 > 6456 [i]