MinT - Best Known (46, 108, s)-Nets in Base 9

Best Known (46, 108, s)-Nets in Base 9

(46, 108, 84)-Net over F₉ — Constructive and digital

Digital (46, 108, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 33, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 75, 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]

(46, 108, 94)-Net in Base 9 — Constructive

(46, 108, 94)-net in base 9, using

base change [i] based on digital (10, 72, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(46, 108, 162)-Net over F₉ — Digital

Digital (46, 108, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(46, 108, 3257)-Net in Base 9 — Upper bound on s

There is no (46, 108, 3258)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 478684 403506 660462 537018 892888 534096 462731 866158 189362 206859 417024 443248 591861 281467 080086 477108 065265 > 9¹⁰⁸ [i]