MinT - Best Known (17, 17+39, s)-Nets in Base 128

Best Known (17, 17+39, s)-Nets in Base 128

Digital (17, 56, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 56, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

Digital (17, 56, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 56, 386)-net over F₁₂₈, using
- net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]

(17, 56, 513)-net in base 128, using

16 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 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]

There is no (17, 56, 78557)-net in base 128, because

1 times m-reduction [i] would yield (17, 55, 78557)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 78 822458 777469 453452 969535 759956 182985 289038 927802 702726 443592 158892 071335 496751 279113 578438 280039 220069 812032 813212 > 128⁵⁵ [i]