Best Known (41−31, 41, s)-Nets in Base 64
(41−31, 41, 177)-Net over F64 — Constructive and digital
Digital (10, 41, 177)-net over F64, using
- t-expansion [i] based on digital (7, 41, 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
(41−31, 41, 192)-Net in Base 64 — Constructive
(10, 41, 192)-net in base 64, using
- 8 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
(41−31, 41, 225)-Net over F64 — Digital
Digital (10, 41, 225)-net over F64, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
(41−31, 41, 6674)-Net in Base 64 — Upper bound on s
There is no (10, 41, 6675)-net in base 64, because
- 1 times m-reduction [i] would yield (10, 40, 6675)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 1 767812 544863 240051 830513 496623 451280 843257 540360 830331 952067 921590 475216 > 6440 [i]