MinT - Best Known (105−60, 105, s)-Nets in Base 9

Best Known (105−60, 105, s)-Nets in Base 9

(105−60, 105, 84)-Net over F₉ — Constructive and digital

Digital (45, 105, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 32, 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, 73, 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]

(105−60, 105, 94)-Net in Base 9 — Constructive

(45, 105, 94)-net in base 9, using

base change [i] based on digital (10, 70, 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]

(105−60, 105, 147)-Net over F₉ — Digital

Digital (45, 105, 147)-net over F₉, using

t-expansion [i] based on digital (43, 105, 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]

(105−60, 105, 3274)-Net in Base 9 — Upper bound on s

There is no (45, 105, 3275)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15763 851006 468176 120937 865563 483985 583371 985430 106247 018377 579421 256656 550849 709825 560333 920532 914129 > 9¹⁰⁵ [i]