MinT - Best Known (14, 14+40, s)-Nets in Base 128

Best Known (14, 14+40, s)-Nets in Base 128

(14, 14+40, 288)-Net over F₁₂₈ — Constructive and digital

Digital (14, 54, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 54, 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+40, 353)-Net over F₁₂₈ — Digital

Digital (14, 54, 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+40, 31977)-Net in Base 128 — Upper bound on s

There is no (14, 54, 31978)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 616025 072263 785009 800918 246774 609994 463571 327521 814452 748245 054746 976467 409063 992183 210305 034553 029130 858403 795996 > 128⁵⁴ [i]