Best Known (78−40, 78, s)-Nets in Base 64
(78−40, 78, 513)-Net over F64 — Constructive and digital
Digital (38, 78, 513)-net over F64, using
- t-expansion [i] based on digital (28, 78, 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
(78−40, 78, 1072)-Net over F64 — Digital
Digital (38, 78, 1072)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6478, 1072, F64, 40) (dual of [1072, 994, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(6478, 1365, F64, 40) (dual of [1365, 1287, 41]-code), using
(78−40, 78, 1459031)-Net in Base 64 — Upper bound on s
There is no (38, 78, 1459032)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 151237 304477 197323 609675 250610 675979 752343 289658 041657 514109 080223 626772 375925 923520 249128 571590 871691 727136 919692 460611 485727 823147 404879 > 6478 [i]