MinT - Best Known (13, 13+43, s)-Nets in Base 128

Best Known (13, 13+43, s)-Nets in Base 128

(13, 13+43, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 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]

(13, 13+43, 321)-Net over F₁₂₈ — Digital

Digital (13, 56, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 56, 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, 13+43, 22561)-Net in Base 128 — Upper bound on s

There is no (13, 56, 22562)-net in base 128, because

1 times m-reduction [i] would yield (13, 55, 22562)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 78 808226 628590 710914 141378 508713 700981 484551 726793 602816 636914 419828 107276 534966 621866 812527 575422 546678 161267 933400 > 128⁵⁵ [i]