MinT - Best Known (9, 9+41, s)-Nets in Base 9

Best Known (9, 9+41, s)-Nets in Base 9

(9, 9+41, 40)-Net over F₉ — Constructive and digital

Digital (9, 50, 40)-net over F₉, using

t-expansion [i] based on digital (8, 50, 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]

(9, 9+41, 48)-Net over F₉ — Digital

Digital (9, 50, 48)-net over F₉, using

net from sequence [i] based on digital (9, 47)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 9 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(9, 9+41, 205)-Net in Base 9 — Upper bound on s

There is no (9, 50, 206)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁰, 206, S₉, 41), but
- the linear programming bound shows that MÂ â‰¥ 3 378891 788350 189965 906499 111363 663774 759601 613197 845059 934852 278682 394934 654474 098165 394331 492169 615562 / 6 464550 992473 111827 444508 125793 966413 820370 554013 521127 > 9⁵⁰ [i]