Best Known (67−40, 67, s)-Nets in Base 256
(67−40, 67, 521)-Net over F256 — Constructive and digital
Digital (27, 67, 521)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (4, 44, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (3, 23, 260)-net over F256, using
(67−40, 67, 1026)-Net over F256 — Digital
Digital (27, 67, 1026)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25667, 1026, F256, 3, 40) (dual of [(1026, 3), 3011, 41]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25664, 1025, F256, 3, 40) (dual of [(1025, 3), 3011, 41]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,3034P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric NRT-code AGe(3;F,3034P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25664, 1025, F256, 3, 40) (dual of [(1025, 3), 3011, 41]-NRT-code), using
(67−40, 67, 3805124)-Net in Base 256 — Upper bound on s
There is no (27, 67, 3805125)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 224946 592230 016320 261772 424132 252418 420897 397703 736695 870599 926026 808512 853790 805717 207315 887547 000649 874398 857686 514513 515241 733842 746718 443629 574902 943813 621876 > 25667 [i]