MinT - Best Known (74−63, 74, s)-Nets in Base 128

Best Known (74−63, 74, s)-Nets in Base 128

(74−63, 74, 288)-Net over F₁₂₈ — Constructive and digital

Digital (11, 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]

(74−63, 74, 296)-Net over F₁₂₈ — Digital

Digital (11, 74, 296)-net over F₁₂₈, using

t-expansion [i] based on digital (10, 74, 296)-net over F₁₂₈, using
- net from sequence [i] based on digital (10, 295)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 10 and N(F) ≥ 296, using
    - a curve from the manYPoints database [i]

(74−63, 74, 8946)-Net in Base 128 — Upper bound on s

There is no (11, 74, 8947)-net in base 128, because

1 times m-reduction [i] would yield (11, 73, 8947)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 6726 762125 887525 925241 582157 936339 339924 888917 936062 572488 497933 981341 881427 079832 524999 250554 740624 902119 975041 991324 745116 958741 420349 836974 837608 434720 > 128⁷³ [i]