Best Known (34, 34+47, s)-Nets in Base 64
(34, 34+47, 513)-Net over F64 — Constructive and digital
Digital (34, 81, 513)-net over F64, using
- t-expansion [i] based on digital (28, 81, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(34, 34+47, 286723)-Net in Base 64 — Upper bound on s
There is no (34, 81, 286724)-net in base 64, because
- 1 times m-reduction [i] would yield (34, 80, 286724)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 121815 300690 864979 368048 910911 478538 278794 712908 033800 638179 382615 396958 983662 622896 220425 748259 885165 238152 656037 178896 559048 505368 602497 165312 > 6480 [i]