MinT - Best Known (86−75, 86, s)-Nets in Base 9

Best Known (86−75, 86, s)-Nets in Base 9

(86−75, 86, 40)-Net over F₉ — Constructive and digital

Digital (11, 86, 40)-net over F₉, using

t-expansion [i] based on digital (8, 86, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(86−75, 86, 55)-Net over F₉ — Digital

Digital (11, 86, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(86−75, 86, 132)-Net in Base 9 — Upper bound on s

There is no (11, 86, 133)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁶, 133, S₉, 75), but
- the linear programming bound shows that MÂ â‰¥ 712 663792 722521 378885 622156 211754 934189 640681 843504 685245 315522 398181 179917 958306 842511 012791 017972 125750 612687 533085 190066 451553 097041 / 60362 446976 193372 021866 288021 728400 548102 383387 880733 > 9⁸⁶ [i]