Best Known (31, 31+58, s)-Nets in Base 64
(31, 31+58, 513)-Net over F64 — Constructive and digital
Digital (31, 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
(31, 31+58, 64682)-Net in Base 64 — Upper bound on s
There is no (31, 89, 64683)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 56242 775265 326584 283387 879771 696843 928902 383353 976529 202729 446519 196522 522382 278258 816300 025858 096704 963729 343744 465876 165306 395281 230290 182947 582072 853374 726960 > 6489 [i]