Best Known (39, 39+52, s)-Nets in Base 64
(39, 39+52, 513)-Net over F64 — Constructive and digital
Digital (39, 91, 513)-net over F64, using
- t-expansion [i] based on digital (28, 91, 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
(39, 39+52, 541)-Net over F64 — Digital
Digital (39, 91, 541)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6491, 541, F64, 2, 52) (dual of [(541, 2), 991, 53]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6489, 540, F64, 2, 52) (dual of [(540, 2), 991, 53]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,1027P) [i] based on function field F/F64 with g(F) = 37 and N(F) ≥ 540, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6489, 540, F64, 2, 52) (dual of [(540, 2), 991, 53]-NRT-code), using
(39, 39+52, 351209)-Net in Base 64 — Upper bound on s
There is no (39, 91, 351210)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 230 350469 016426 455338 335837 884030 188148 841006 150859 354979 866483 442469 054808 012348 787027 664907 634384 322077 889093 524716 464272 232428 325867 715461 615554 611756 203904 863088 > 6491 [i]