Best Known (55−45, 55, s)-Nets in Base 256
(55−45, 55, 267)-Net over F256 — Constructive and digital
Digital (10, 55, 267)-net over F256, using
- net from sequence [i] based on digital (10, 266)-sequence over F256, using
(55−45, 55, 513)-Net over F256 — Digital
Digital (10, 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
(55−45, 55, 28926)-Net in Base 256 — Upper bound on s
There is no (10, 55, 28927)-net in base 256, because
- 1 times m-reduction [i] would yield (10, 54, 28927)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 11099 101087 379771 686234 904490 844633 477770 789799 683431 608179 082993 622945 417697 150655 714078 993189 023443 210081 345283 931448 094175 409671 > 25654 [i]