MinT - Best Known (54, 54+47, s)-Nets in Base 9

Best Known (54, 54+47, s)-Nets in Base 9

(54, 54+47, 232)-Net over F₉ — Constructive and digital

Digital (54, 101, 232)-net over F₉, using

3 times m-reduction [i] based on digital (54, 104, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 52, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(54, 54+47, 272)-Net over F₉ — Digital

Digital (54, 101, 272)-net over F₉, using

1 times m-reduction [i] based on digital (54, 102, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 51, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(54, 54+47, 16591)-Net in Base 9 — Upper bound on s

There is no (54, 101, 16592)-net in base 9, because

1 times m-reduction [i] would yield (54, 100, 16592)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 265823 743732 821405 107602 111578 959720 583250 680717 495499 194797 599288 328353 748041 300126 227815 286657 > 9¹⁰⁰ [i]