MinT - Best Known (11, 11+45, s)-Nets in Base 9

Best Known (11, 11+45, s)-Nets in Base 9

(11, 11+45, 40)-Net over F₉ — Constructive and digital

Digital (11, 56, 40)-net over F₉, using

t-expansion [i] based on digital (8, 56, 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]

(11, 11+45, 55)-Net over F₉ — Digital

Digital (11, 56, 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]

(11, 11+45, 252)-Net in Base 9 — Upper bound on s

There is no (11, 56, 253)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁶, 253, S₉, 45), but
- the linear programming bound shows that MÂ â‰¥ 14050 413158 089014 667096 845569 204561 136544 466572 675888 540662 732528 409097 562901 059332 582479 625210 442531 532800 / 49643 820062 566366 640194 027971 128601 762587 331729 491111 > 9⁵⁶ [i]