MinT - Best Known (92−49, 92, s)-Nets in Base 9

Best Known (92−49, 92, s)-Nets in Base 9

(92−49, 92, 98)-Net over F₉ — Constructive and digital

Digital (43, 92, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 30, 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 (13, 62, 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]

(92−49, 92, 147)-Net over F₉ — Digital

Digital (43, 92, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(92−49, 92, 5072)-Net in Base 9 — Upper bound on s

There is no (43, 92, 5073)-net in base 9, because

1 times m-reduction [i] would yield (43, 91, 5073)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 687 915192 898621 859357 762208 399015 503786 902089 393559 639380 267311 198094 445404 057156 463041 > 9⁹¹ [i]