MinT - Best Known (111−64, 111, s)-Nets in Base 9

Best Known (111−64, 111, s)-Nets in Base 9

(111−64, 111, 84)-Net over F₉ — Constructive and digital

Digital (47, 111, 84)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 34, 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, 77, 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]

(111−64, 111, 94)-Net in Base 9 — Constructive

(47, 111, 94)-net in base 9, using

base change [i] based on digital (10, 74, 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]

(111−64, 111, 162)-Net over F₉ — Digital

Digital (47, 111, 162)-net over F₉, using

t-expansion [i] based on digital (46, 111, 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]

(111−64, 111, 3245)-Net in Base 9 — Upper bound on s

There is no (47, 111, 3246)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8413 016573 576365 412808 676556 976059 801775 741802 192260 150520 878365 284370 878408 473722 813929 752660 617355 676161 > 9¹¹¹ [i]