MinT - Best Known (116−66, 116, s)-Nets in Base 9

Best Known (116−66, 116, s)-Nets in Base 9

(116−66, 116, 94)-Net over F₉ — Constructive and digital

Digital (50, 116, 94)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 37, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]
2. digital (13, 79, 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]

(116−66, 116, 96)-Net in Base 9 — Constructive

(50, 116, 96)-net in base 9, using

1 times m-reduction [i] based on (50, 117, 96)-net in base 9, using
- base change [i] based on digital (11, 78, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(116−66, 116, 182)-Net over F₉ — Digital

Digital (50, 116, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(116−66, 116, 3700)-Net in Base 9 — Upper bound on s

There is no (50, 116, 3701)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 495 919203 708732 349452 361025 969467 015827 146466 992104 670067 595154 474703 046462 427634 036892 614062 495018 981177 959593 > 9¹¹⁶ [i]