MinT - Best Known (11, 11+39, s)-Nets in Base 256

Best Known (11, 11+39, s)-Nets in Base 256

(11, 11+39, 268)-Net over F₂₅₆ — Constructive and digital

Digital (11, 50, 268)-net over F₂₅₆, using

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

(11, 11+39, 513)-Net over F₂₅₆ — Digital

Digital (11, 50, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 50, 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]

(11, 11+39, 50503)-Net in Base 256 — Upper bound on s

There is no (11, 50, 50504)-net in base 256, because

1 times m-reduction [i] would yield (11, 49, 50504)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 10088 834826 314911 567008 651695 333127 200483 281416 718302 651219 541499 027803 784590 116852 459854 002370 057699 536278 586509 847756 > 256⁴⁹ [i]