MinT - Best Known (54, 54+68, s)-Nets in Base 16

Best Known (54, 54+68, s)-Nets in Base 16

(54, 54+68, 243)-Net over F₁₆ — Constructive and digital

Digital (54, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(54, 54+68, 257)-Net over F₁₆ — Digital

Digital (54, 122, 257)-net over F₁₆, using

net from sequence [i] based on digital (54, 256)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 54 and N(F) ≥ 257, using
  - Drinfeld modules of rank 1 [i]

(54, 54+68, 18863)-Net in Base 16 — Upper bound on s

There is no (54, 122, 18864)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 800 139784 389903 812010 566586 676409 796177 746409 576863 813529 829027 861982 820573 969414 684859 319688 262840 034964 381434 405743 083744 416285 528669 158767 638641 > 16¹²² [i]