MinT - Best Known (54, 54+39, s)-Nets in Base 16

Best Known (54, 54+39, s)-Nets in Base 16

(54, 54+39, 528)-Net over F₁₆ — Constructive and digital

Digital (54, 93, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (54, 94, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 47, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(54, 54+39, 905)-Net over F₁₆ — Digital

Digital (54, 93, 905)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+39, 357756)-Net in Base 16 — Upper bound on s

There is no (54, 93, 357757)-net in base 16, because

1 times m-reduction [i] would yield (54, 92, 357757)-net in base 16, but
- 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]