MinT - Best Known (44, 44+81, s)-Nets in Base 16

Best Known (44, 44+81, s)-Nets in Base 16

(44, 44+81, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 125, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 125, 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]

(44, 44+81, 226)-Net over F₁₆ — Digital

Digital (44, 125, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 125, 226)-net over F₁₆, using
- net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
    - Drinfeld modules of rank 1 [i]

(44, 44+81, 5659)-Net in Base 16 — Upper bound on s

There is no (44, 125, 5660)-net in base 16, because

1 times m-reduction [i] would yield (44, 124, 5660)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 205351 747166 965234 199278 750077 156936 217007 575514 514602 575516 556611 996094 887812 051644 525739 415399 270961 178789 104592 922443 907957 274895 968737 856256 495376 > 16¹²⁴ [i]