Best Known (68−41, 68, s)-Nets in Base 256
(68−41, 68, 521)-Net over F256 — Constructive and digital
Digital (27, 68, 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, 45, 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
(68−41, 68, 1025)-Net over F256 — Digital
Digital (27, 68, 1025)-net over F256, using
- t-expansion [i] based on digital (24, 68, 1025)-net over F256, using
- net from sequence [i] based on digital (24, 1024)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [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]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- net from sequence [i] based on digital (24, 1024)-sequence over F256, using
(68−41, 68, 3805124)-Net in Base 256 — Upper bound on s
There is no (27, 68, 3805125)-net in base 256, because
- 1 times m-reduction [i] would yield (27, 67, 3805125)-net in base 256, but
- 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]