MinT - Best Known (66−55, 66, s)-Nets in Base 256

Best Known (66−55, 66, s)-Nets in Base 256

(66−55, 66, 268)-Net over F₂₅₆ — Constructive and digital

Digital (11, 66, 268)-net over F₂₅₆, using

net from sequence [i] based on digital (11, 267)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(66−55, 66, 513)-Net over F₂₅₆ — Digital

Digital (11, 66, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 66, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(66−55, 66, 26870)-Net in Base 256 — Upper bound on s

There is no (11, 66, 26871)-net in base 256, because

1 times m-reduction [i] would yield (11, 65, 26871)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 435442 549902 720240 746841 979583 573649 946242 603588 385542 282376 388441 054682 297811 357944 576197 181477 664413 600101 342023 599577 314373 388866 072076 748146 801451 330736 > 256⁶⁵ [i]