MinT - Best Known (58−47, 58, s)-Nets in Base 9

Best Known (58−47, 58, s)-Nets in Base 9

(58−47, 58, 40)-Net over F₉ — Constructive and digital

Digital (11, 58, 40)-net over F₉, using

t-expansion [i] based on digital (8, 58, 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]

(58−47, 58, 55)-Net over F₉ — Digital

Digital (11, 58, 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]

(58−47, 58, 244)-Net in Base 9 — Upper bound on s

There is no (11, 58, 245)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁸, 245, S₉, 47), but
- the linear programming bound shows that MÂ â‰¥ 20772 374140 876250 490557 177497 773514 066953 443098 778175 448351 180720 470213 744198 068018 507977 753553 027557 946958 798639 893478 916128 / 877 691531 593589 873282 923362 778161 069476 455827 882122 374165 602062 275303 > 9⁵⁸ [i]