Best Known (30, 30+59, s)-Nets in Base 64
(30, 30+59, 513)-Net over F64 — Constructive and digital
Digital (30, 89, 513)-net over F64, using
- t-expansion [i] based on digital (28, 89, 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
(30, 30+59, 56039)-Net in Base 64 — Upper bound on s
There is no (30, 89, 56040)-net in base 64, because
- 1 times m-reduction [i] would yield (30, 88, 56040)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 879 087369 421488 561128 199122 498898 585565 458234 186802 230260 879695 622250 009628 170890 650524 364323 250200 893116 796274 924941 728915 074918 961068 201705 940814 844711 200932 > 6488 [i]