MinT - Best Known (54, 54+59, s)-Nets in Base 16

Best Known (54, 54+59, s)-Nets in Base 16

(54, 54+59, 243)-Net over F₁₆ — Constructive and digital

Digital (54, 113, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 113, 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+59, 319)-Net over F₁₆ — Digital

Digital (54, 113, 319)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+59, 34771)-Net in Base 16 — Upper bound on s

There is no (54, 113, 34772)-net in base 16, because

1 times m-reduction [i] would yield (54, 112, 34772)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 727 004790 594526 974922 196763 283039 240781 589883 831752 742212 439593 927318 693721 001825 955758 267570 792412 110212 339358 547493 616871 000626 664496 > 16¹¹² [i]