MinT - Best Known (14, 14+44, s)-Nets in Base 128

Best Known (14, 14+44, s)-Nets in Base 128

(14, 14+44, 288)-Net over F₁₂₈ — Constructive and digital

Digital (14, 58, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 58, 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]

(14, 14+44, 353)-Net over F₁₂₈ — Digital

Digital (14, 58, 353)-net over F₁₂₈, using

net from sequence [i] based on digital (14, 352)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 14 and N(F) ≥ 353, using
  - a curve from the manYPoints database [i]

(14, 14+44, 25600)-Net in Base 128 — Upper bound on s

There is no (14, 58, 25601)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 165 405480 849239 550068 653035 941929 847354 320746 087355 573099 699210 678038 702542 723847 562164 743297 466826 567114 756101 829981 284864 > 128⁵⁸ [i]