MinT - Best Known (11, 78, s)-Nets in Base 128

Best Known (11, 78, s)-Nets in Base 128

(11, 78, 288)-Net over F₁₂₈ — Constructive and digital

Digital (11, 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]

(11, 78, 296)-Net over F₁₂₈ — Digital

Digital (11, 78, 296)-net over F₁₂₈, using

t-expansion [i] based on digital (10, 78, 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]

(11, 78, 8541)-Net in Base 128 — Upper bound on s

There is no (11, 78, 8542)-net in base 128, because

1 times m-reduction [i] would yield (11, 77, 8542)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 801141 640241 130437 975477 272077 030870 327001 762945 673232 587904 579429 670679 288553 077157 931633 156070 613317 001093 681961 774519 443466 575148 184019 306105 173352 163418 364950 > 128⁷⁷ [i]