MinT - Best Known (15, 15+33, s)-Nets in Base 256

Best Known (15, 15+33, s)-Nets in Base 256

(15, 15+33, 272)-Net over F₂₅₆ — Constructive and digital

Digital (15, 48, 272)-net over F₂₅₆, using

net from sequence [i] based on digital (15, 271)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(15, 15+33, 513)-Net over F₂₅₆ — Digital

Digital (15, 48, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 48, 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]

(15, 15+33, 316368)-Net in Base 256 — Upper bound on s

There is no (15, 48, 316369)-net in base 256, because

1 times m-reduction [i] would yield (15, 47, 316369)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 153918 969252 440055 515811 914201 692867 369771 106200 609998 491426 410731 270325 667024 685545 946019 817320 700655 618479 968021 > 256⁴⁷ [i]