Best Known (55−40, 55, s)-Nets in Base 256
(55−40, 55, 272)-Net over F256 — Constructive and digital
Digital (15, 55, 272)-net over F256, using
- net from sequence [i] based on digital (15, 271)-sequence over F256, using
(55−40, 55, 513)-Net over F256 — Digital
Digital (15, 55, 513)-net over F256, using
- t-expansion [i] based on digital (8, 55, 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
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
(55−40, 55, 136582)-Net in Base 256 — Upper bound on s
There is no (15, 55, 136583)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 2 839363 843080 260766 807720 511681 626463 428013 414343 765742 117993 563334 100795 122233 240955 703444 215517 260825 557217 694527 932280 075669 341176 > 25655 [i]