MinT - Best Known (76−39, 76, s)-Nets in Base 9

Best Known (76−39, 76, s)-Nets in Base 9

(76−39, 76, 96)-Net over F₉ — Constructive and digital

Digital (37, 76, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 24, 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, 52, 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]

(76−39, 76, 143)-Net over F₉ — Digital

Digital (37, 76, 143)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−39, 76, 5781)-Net in Base 9 — Upper bound on s

There is no (37, 76, 5782)-net in base 9, because

1 times m-reduction [i] would yield (37, 75, 5782)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 370942 603881 551432 325204 813594 383401 878864 753706 217129 721071 741870 123217 > 9⁷⁵ [i]