MinT - Best Known (50, 50+55, s)-Nets in Base 9

Best Known (50, 50+55, s)-Nets in Base 9

(50, 50+55, 108)-Net over F₉ — Constructive and digital

Digital (50, 105, 108)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 33, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (17, 72, 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+55, 182)-Net over F₉ — Digital

Digital (50, 105, 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+55, 6453)-Net in Base 9 — Upper bound on s

There is no (50, 105, 6454)-net in base 9, because

1 times m-reduction [i] would yield (50, 104, 6454)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1743 892667 326726 233144 819528 982746 398083 798376 731883 194877 513440 628924 106153 396604 762191 023344 106065 > 9¹⁰⁴ [i]