MinT - Best Known (13, 13+25, s)-Nets in Base 128

Best Known (13, 13+25, s)-Nets in Base 128

Digital (13, 38, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 38, 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 (13, 38, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 38, 321)-net over F₁₂₈, using
- net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
    - a curve from the manYPoints database [i]

(13, 38, 513)-net in base 128, using

2 times m-reduction [i] based on (13, 40, 513)-net in base 128, using
- base change [i] based on digital (8, 35, 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 (13, 38, 130849)-net in base 128, because

1 times m-reduction [i] would yield (13, 37, 130849)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 926350 620156 389942 764733 621156 808465 826880 282442 454606 364741 555980 286179 267592 > 128³⁷ [i]