Best Known (42−30, 42, s)-Nets in Base 256
(42−30, 42, 269)-Net over F256 — Constructive and digital
Digital (12, 42, 269)-net over F256, using
- net from sequence [i] based on digital (12, 268)-sequence over F256, using
(42−30, 42, 513)-Net over F256 — Digital
Digital (12, 42, 513)-net over F256, using
- t-expansion [i] based on digital (8, 42, 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
(42−30, 42, 139404)-Net in Base 256 — Upper bound on s
There is no (12, 42, 139405)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 139993 607515 804010 263908 207950 453503 500160 879334 336678 964703 085896 778760 446830 256318 773571 795504 085376 > 25642 [i]