MinT - Best Known (76−51, 76, s)-Nets in Base 128

Best Known (76−51, 76, s)-Nets in Base 128

(76−51, 76, 288)-Net over F₁₂₈ — Constructive and digital

Digital (25, 76, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 76, 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]

(76−51, 76, 513)-Net over F₁₂₈ — Digital

Digital (25, 76, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 76, 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]

(76−51, 76, 168043)-Net in Base 128 — Upper bound on s

There is no (25, 76, 168044)-net in base 128, because

1 times m-reduction [i] would yield (25, 75, 168044)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 109 852668 869311 285504 748192 454399 335462 448342 056861 896597 611948 329619 604008 059635 174975 551007 374725 697020 032490 819435 004741 897911 670196 846794 186154 601943 284790 > 128⁷⁵ [i]