MinT - Best Known (10, 56, s)-Nets in Base 9

Best Known (10, 56, s)-Nets in Base 9

(10, 56, 40)-Net over F₉ — Constructive and digital

Digital (10, 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]

(10, 56, 54)-Net over F₉ — Digital

Digital (10, 56, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 56, 219)-Net in Base 9 — Upper bound on s

There is no (10, 56, 220)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁶, 220, S₉, 46), but
- the linear programming bound shows that MÂ â‰¥ 1381 926249 747888 722737 662587 267524 632637 049370 891467 199892 685283 810943 157848 400467 691655 959170 590477 490401 494102 529483 626889 / 4760 092817 388985 803584 111604 946264 881107 718401 243117 072357 310156 164393 > 9⁵⁶ [i]