Best Known (51−43, 51, s)-Nets in Base 256
(51−43, 51, 265)-Net over F256 — Constructive and digital
Digital (8, 51, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(51−43, 51, 513)-Net over F256 — Digital
Digital (8, 51, 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
(51−43, 51, 18434)-Net in Base 256 — Upper bound on s
There is no (8, 51, 18435)-net in base 256, because
- 1 times m-reduction [i] would yield (8, 50, 18435)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 2 585186 826961 581283 817632 862897 254277 337362 981054 231125 031439 832793 931953 925417 889878 705981 058728 112713 038127 898833 458176 > 25650 [i]