MinT - Best Known (77−69, 77, s)-Nets in Base 128

Best Known (77−69, 77, s)-Nets in Base 128

(77−69, 77, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 77, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 77, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(77−69, 77, 276)-Net over F₁₂₈ — Digital

Digital (8, 77, 276)-net over F₁₂₈, using

net from sequence [i] based on digital (8, 275)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 8 and N(F) ≥ 276, using
  - a curve from the manYPoints database [i]

(77−69, 77, 5452)-Net in Base 128 — Upper bound on s

There is no (8, 77, 5453)-net in base 128, because

1 times m-reduction [i] would yield (8, 76, 5453)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14127 912849 260022 354553 457727 289373 616072 096835 300055 617937 156119 398997 422906 330044 365326 875874 824109 998609 944631 644570 702984 184347 906711 218513 120142 686294 640908 > 128⁷⁶ [i]