MinT - Best Known (50, 50+61, s)-Nets in Base 9

Best Known (50, 50+61, s)-Nets in Base 9

(50, 50+61, 102)-Net over F₉ — Constructive and digital

Digital (50, 111, 102)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 33, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (17, 78, 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+61, 182)-Net over F₉ — Digital

Digital (50, 111, 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+61, 4730)-Net in Base 9 — Upper bound on s

There is no (50, 111, 4731)-net in base 9, because

1 times m-reduction [i] would yield (50, 110, 4731)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 928 396704 915680 011708 961628 466529 467477 077570 400506 533676 861474 501774 779956 710738 193420 310134 113455 702737 > 9¹¹⁰ [i]