MinT - Best Known (54, 100, s)-Nets in Base 9

Best Known (54, 100, s)-Nets in Base 9

(54, 100, 300)-Net over F₉ — Constructive and digital

Digital (54, 100, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 50, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(54, 100, 308)-Net over F₉ — Digital

Digital (54, 100, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 50, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(54, 100, 16591)-Net in Base 9 — Upper bound on s

There is no (54, 100, 16592)-net in base 9, because

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]