Best Known (32, 32+38, s)-Nets in Base 64
(32, 32+38, 513)-Net over F64 — Constructive and digital
Digital (32, 70, 513)-net over F64, using
- t-expansion [i] based on digital (28, 70, 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
(32, 32+38, 626)-Net over F64 — Digital
Digital (32, 70, 626)-net over F64, using
(32, 32+38, 567825)-Net in Base 64 — Upper bound on s
There is no (32, 70, 567826)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2 707704 087205 317099 063829 164915 825642 666570 701264 443704 497106 440635 085827 923826 475192 090188 349895 278504 281238 600166 645544 447744 > 6470 [i]