MinT - Best Known (95−83, 95, s)-Nets in Base 9

Best Known (95−83, 95, s)-Nets in Base 9

(95−83, 95, 40)-Net over F₉ — Constructive and digital

Digital (12, 95, 40)-net over F₉, using

t-expansion [i] based on digital (8, 95, 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]

(95−83, 95, 56)-Net over F₉ — Digital

Digital (12, 95, 56)-net over F₉, using

net from sequence [i] based on digital (12, 55)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 12 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(95−83, 95, 129)-Net in Base 9 — Upper bound on s

There is no (12, 95, 130)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹⁵, 130, S₉, 83), but
- the linear programming bound shows that MÂ â‰¥ 134 818938 381334 064090 780951 748446 852388 278203 495663 430396 225297 876054 146478 257633 760050 833840 255111 067023 742040 732222 619223 969275 / 26 548321 724997 251895 709272 066492 964987 > 9⁹⁵ [i]