MinT - Best Known (47, 96, s)-Nets in Base 9

Best Known (47, 96, s)-Nets in Base 9

(47, 96, 108)-Net over F₉ — Constructive and digital

Digital (47, 96, 108)-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 (17, 66, 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]

(47, 96, 176)-Net over F₉ — Digital

Digital (47, 96, 176)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 96, 7321)-Net in Base 9 — Upper bound on s

There is no (47, 96, 7322)-net in base 9, because

1 times m-reduction [i] would yield (47, 95, 7322)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 499621 636961 042013 074690 836083 601233 582784 650601 508057 868728 249922 378897 006831 000934 346369 > 9⁹⁵ [i]