MinT - Best Known (26, 26+52, s)-Nets in Base 128

Best Known (26, 26+52, s)-Nets in Base 128

(26, 26+52, 288)-Net over F₁₂₈ — Constructive and digital

Digital (26, 78, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 78, 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]

(26, 26+52, 513)-Net over F₁₂₈ — Digital

Digital (26, 78, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 78, 513)-net over F₁₂₈, using
- net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
    - a curve from the manYPoints database [i]

(26, 26+52, 174215)-Net in Base 128 — Upper bound on s

There is no (26, 78, 174216)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 230 351005 917765 030821 648267 211785 493570 459473 971366 220612 562027 855272 335777 081599 103231 646195 944224 518504 209961 406034 604924 546508 365094 842845 740603 430303 387221 342512 > 128⁷⁸ [i]