Best Known (53−39, 53, s)-Nets in Base 256
(53−39, 53, 271)-Net over F256 — Constructive and digital
Digital (14, 53, 271)-net over F256, using
- net from sequence [i] based on digital (14, 270)-sequence over F256, using
(53−39, 53, 513)-Net over F256 — Digital
Digital (14, 53, 513)-net over F256, using
- t-expansion [i] based on digital (8, 53, 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
(53−39, 53, 121231)-Net in Base 256 — Upper bound on s
There is no (14, 53, 121232)-net in base 256, because
- 1 times m-reduction [i] would yield (14, 52, 121232)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 169244 496534 876428 711525 711817 425509 034794 987323 730611 754702 962988 021444 517815 118606 092500 290896 999133 029354 901062 209799 542616 > 25652 [i]