Best Known (56−47, 56, s)-Nets in Base 256
(56−47, 56, 266)-Net over F256 — Constructive and digital
Digital (9, 56, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(56−47, 56, 513)-Net over F256 — Digital
Digital (9, 56, 513)-net over F256, using
- t-expansion [i] based on digital (8, 56, 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
(56−47, 56, 21209)-Net in Base 256 — Upper bound on s
There is no (9, 56, 21210)-net in base 256, because
- 1 times m-reduction [i] would yield (9, 55, 21210)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 2 841751 580765 662615 561118 920264 742351 386390 107765 554167 697470 293904 417426 606714 361510 492622 075875 685544 094401 725255 752738 176092 598276 > 25655 [i]