MinT - Best Known (73−37, 73, s)-Nets in Base 9

Best Known (73−37, 73, s)-Nets in Base 9

(73−37, 73, 96)-Net over F₉ — Constructive and digital

Digital (36, 73, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 23, 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, 50, 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]

(73−37, 73, 146)-Net over F₉ — Digital

Digital (36, 73, 146)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−37, 73, 6183)-Net in Base 9 — Upper bound on s

There is no (36, 73, 6184)-net in base 9, because

1 times m-reduction [i] would yield (36, 72, 6184)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 808240 454412 916484 027050 104637 700501 391280 822471 087864 256493 165441 > 9⁷² [i]