MinT - Best Known (87−76, 87, s)-Nets in Base 9

Best Known (87−76, 87, s)-Nets in Base 9

(87−76, 87, 40)-Net over F₉ — Constructive and digital

Digital (11, 87, 40)-net over F₉, using

t-expansion [i] based on digital (8, 87, 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]

(87−76, 87, 55)-Net over F₉ — Digital

Digital (11, 87, 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]

(87−76, 87, 129)-Net in Base 9 — Upper bound on s

There is no (11, 87, 130)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁷, 130, S₉, 76), but
- the linear programming bound shows that MÂ â‰¥ 1 297069 894639 276603 608601 613678 467908 214948 217730 188833 749400 215297 823656 905135 524191 849356 344061 792822 103627 408337 181983 809556 400650 247259 / 11 967843 315364 215156 477020 078398 965175 561891 874813 020955 > 9⁸⁷ [i]