Best Known (58−40, 58, s)-Nets in Base 64
(58−40, 58, 177)-Net over F64 — Constructive and digital
Digital (18, 58, 177)-net over F64, using
- t-expansion [i] based on digital (7, 58, 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
(58−40, 58, 281)-Net over F64 — Digital
Digital (18, 58, 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
(58−40, 58, 288)-Net in Base 64 — Constructive
(18, 58, 288)-net in base 64, using
- 5 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
(58−40, 58, 321)-Net in Base 64
(18, 58, 321)-net in base 64, using
- 6 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
(58−40, 58, 22787)-Net in Base 64 — Upper bound on s
There is no (18, 58, 22788)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 573 523850 197275 094835 530097 515380 602163 459585 774520 411831 490209 874698 138143 741802 957613 870135 458837 224256 > 6458 [i]