MinT - Best Known (58, 139, s)-Nets in Base 9

Best Known (58, 139, s)-Nets in Base 9

(58, 139, 96)-Net over F₉ — Constructive and digital

Digital (58, 139, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 45, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 94, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(58, 139, 182)-Net over F₉ — Digital

Digital (58, 139, 182)-net over F₉, using

t-expansion [i] based on digital (50, 139, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(58, 139, 3837)-Net in Base 9 — Upper bound on s

There is no (58, 139, 3838)-net in base 9, because

1 times m-reduction [i] would yield (58, 138, 3838)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485835 589092 417091 441932 515602 227362 206127 806254 989979 037641 808756 658779 830125 676191 418905 324229 783292 049647 237502 268819 555277 602945 > 9¹³⁸ [i]