MinT - Best Known (54, 54+38, s)-Nets in Base 16

Best Known (54, 54+38, s)-Nets in Base 16

(54, 54+38, 530)-Net over F₁₆ — Constructive and digital

Digital (54, 92, 530)-net over F₁₆, using

trace code for nets [i] based on digital (8, 46, 265)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(54, 54+38, 1026)-Net over F₁₆ — Digital

Digital (54, 92, 1026)-net over F₁₆, using

trace code for nets [i] based on digital (8, 46, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(54, 54+38, 357756)-Net in Base 16 — Upper bound on s

There is no (54, 92, 357757)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 601 244000 444476 861930 758751 434919 292812 911430 841565 012158 103078 139239 971962 746440 724531 965858 670821 671027 905796 > 16⁹² [i]