Best Known (58−30, 58, s)-Nets in Base 64
(58−30, 58, 513)-Net over F64 — Constructive and digital
Digital (28, 58, 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
(58−30, 58, 840)-Net over F64 — Digital
Digital (28, 58, 840)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6458, 840, F64, 30) (dual of [840, 782, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(6458, 1365, F64, 30) (dual of [1365, 1307, 31]-code), using
(58−30, 58, 982468)-Net in Base 64 — Upper bound on s
There is no (28, 58, 982469)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 573 375936 250545 675876 661006 314706 405519 726018 567242 556188 621346 244717 813319 221217 608041 128318 169202 817472 > 6458 [i]