Best Known (12, 45, s)-Nets in Base 256
(12, 45, 269)-Net over F256 — Constructive and digital
Digital (12, 45, 269)-net over F256, using
- net from sequence [i] based on digital (12, 268)-sequence over F256, using
(12, 45, 513)-Net over F256 — Digital
Digital (12, 45, 513)-net over F256, using
- t-expansion [i] based on digital (8, 45, 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
(12, 45, 111848)-Net in Base 256 — Upper bound on s
There is no (12, 45, 111849)-net in base 256, because
- 1 times m-reduction [i] would yield (12, 44, 111849)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 9175 015408 733396 550918 634900 077155 080128 585197 682164 687631 076688 950032 461656 564242 091174 304825 670842 772046 > 25644 [i]