MinT - Best Known (50, 50+53, s)-Nets in Base 9

Best Known (50, 50+53, s)-Nets in Base 9

(50, 50+53, 110)-Net over F₉ — Constructive and digital

Digital (50, 103, 110)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (7, 33, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]
2. digital (17, 70, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(50, 50+53, 182)-Net over F₉ — Digital

Digital (50, 103, 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]

(50, 50+53, 7291)-Net in Base 9 — Upper bound on s

There is no (50, 103, 7292)-net in base 9, because

1 times m-reduction [i] would yield (50, 102, 7292)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 531820 945885 870606 303148 805744 581767 807057 608801 100764 266736 073906 222997 626216 357317 031435 009089 > 9¹⁰² [i]