Best Known (58−43, 58, s)-Nets in Base 256
(58−43, 58, 272)-Net over F256 — Constructive and digital
Digital (15, 58, 272)-net over F256, using
- net from sequence [i] based on digital (15, 271)-sequence over F256, using
(58−43, 58, 513)-Net over F256 — Digital
Digital (15, 58, 513)-net over F256, using
- t-expansion [i] based on digital (8, 58, 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
(58−43, 58, 117102)-Net in Base 256 — Upper bound on s
There is no (15, 58, 117103)-net in base 256, because
- 1 times m-reduction [i] would yield (15, 57, 117103)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 186085 916919 772850 828540 047788 063081 606620 923080 759757 916275 990460 918094 743435 006494 585722 856086 081476 575528 933727 735710 337422 611075 249316 > 25657 [i]