MinT - Best Known (125−79, 125, s)-Nets in Base 16

Best Known (125−79, 125, s)-Nets in Base 16

(125−79, 125, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 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]

(125−79, 125, 243)-Net over F₁₆ — Digital

Digital (46, 125, 243)-net over F₁₆, using

net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(125−79, 125, 6893)-Net in Base 16 — Upper bound on s

There is no (46, 125, 6894)-net in base 16, because

1 times m-reduction [i] would yield (46, 124, 6894)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 204784 806600 505787 340744 533516 856644 760061 308844 854217 581185 290725 704799 779285 550568 711358 301812 005706 179304 485492 037612 817162 756721 560567 379717 700116 > 16¹²⁴ [i]