MinT - Best Known (39, 87, s)-Nets in Base 9

Best Known (39, 87, s)-Nets in Base 9

(39, 87, 84)-Net over F₉ — Constructive and digital

Digital (39, 87, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 26, 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, 61, 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]

(39, 87, 94)-Net in Base 9 — Constructive

(39, 87, 94)-net in base 9, using

base change [i] based on digital (10, 58, 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]

(39, 87, 140)-Net over F₉ — Digital

Digital (39, 87, 140)-net over F₉, using

net from sequence [i] based on digital (39, 139)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
  - a curve from the manYPoints database [i]

(39, 87, 3512)-Net in Base 9 — Upper bound on s

There is no (39, 87, 3513)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104860 049842 617373 274856 241220 234792 049464 416658 180967 078127 724370 258914 672598 057921 > 9⁸⁷ [i]