MinT - Best Known (94−51, 94, s)-Nets in Base 9

Best Known (94−51, 94, s)-Nets in Base 9

(94−51, 94, 96)-Net over F₉ — Constructive and digital

Digital (43, 94, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 30, 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, 64, 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]

(94−51, 94, 147)-Net over F₉ — Digital

Digital (43, 94, 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]

(94−51, 94, 4496)-Net in Base 9 — Upper bound on s

There is no (43, 94, 4497)-net in base 9, because

1 times m-reduction [i] would yield (43, 93, 4497)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55730 859549 042452 944472 153921 213267 172067 621890 333626 245393 339913 464962 552981 127969 645641 > 9⁹³ [i]