MinT - Best Known (24, 24+50, s)-Nets in Base 128

Best Known (24, 24+50, s)-Nets in Base 128

(24, 24+50, 288)-Net over F₁₂₈ — Constructive and digital

Digital (24, 74, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 74, 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]

(24, 24+50, 513)-Net over F₁₂₈ — Digital

Digital (24, 74, 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]

(24, 24+50, 138396)-Net in Base 128 — Upper bound on s

There is no (24, 74, 138397)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 858165 484343 526909 235365 757495 689727 573133 935466 642427 607911 386961 180355 440223 721829 886838 078075 257939 225836 639114 504926 503369 496628 545930 926141 590477 151828 > 128⁷⁴ [i]