Best Known (59−35, 59, s)-Nets in Base 256
(59−35, 59, 521)-Net over F256 — Constructive and digital
Digital (24, 59, 521)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (4, 39, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (3, 20, 260)-net over F256, using
(59−35, 59, 1025)-Net over F256 — Digital
Digital (24, 59, 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
(59−35, 59, 4631827)-Net in Base 256 — Upper bound on s
There is no (24, 59, 4631828)-net in base 256, because
- 1 times m-reduction [i] would yield (24, 58, 4631828)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 47 634171 320371 437601 297228 250492 153722 409091 197873 361889 697686 617659 426510 523546 036355 008694 566600 434166 301419 476808 476338 535495 636838 939781 > 25658 [i]