MinT - Best Known (41, 41+83, s)-Nets in Base 16

Best Known (41, 41+83, s)-Nets in Base 16

(41, 41+83, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 124, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 124, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(41, 41+83, 4384)-Net in Base 16 — Upper bound on s

There is no (41, 124, 4385)-net in base 16, because

1 times m-reduction [i] would yield (41, 123, 4385)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12823 986853 576996 153720 342191 912040 100732 081072 655605 464030 055785 051393 740326 432268 475629 632989 135025 017229 618989 570633 125097 362934 202713 983114 731776 > 16¹²³ [i]