MinT - Best Known (43, 43+53, s)-Nets in Base 16

Best Known (43, 43+53, s)-Nets in Base 16

(43, 43+53, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 96, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 96, 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]

(43, 43+53, 226)-Net over F₁₆ — Digital

Digital (43, 96, 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]

(43, 43+53, 17640)-Net in Base 16 — Upper bound on s

There is no (43, 96, 17641)-net in base 16, because

1 times m-reduction [i] would yield (43, 95, 17641)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 462985 499868 252974 745534 500783 146517 664308 853139 714906 506839 667057 009787 408029 178670 011157 901375 530530 086093 865616 > 16⁹⁵ [i]