Best Known (65−57, 65, s)-Nets in Base 256
(65−57, 65, 265)-Net over F256 — Constructive and digital
Digital (8, 65, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(65−57, 65, 513)-Net over F256 — Digital
Digital (8, 65, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 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) = 8 and N(F) ≥ 513, using
(65−57, 65, 14144)-Net in Base 256 — Upper bound on s
There is no (8, 65, 14145)-net in base 256, because
- 1 times m-reduction [i] would yield (8, 64, 14145)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 13414 031785 387666 494763 905708 228442 571391 040908 486566 456069 789982 407533 036734 829236 702358 701340 388086 070355 889581 196780 658059 808846 398540 934667 582339 644176 > 25664 [i]