MinT - Best Known (45, 111, s)-Nets in Base 16

Best Known (45, 111, s)-Nets in Base 16

(45, 111, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 111, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 111, 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]

(45, 111, 242)-Net over F₁₆ — Digital

Digital (45, 111, 242)-net over F₁₆, using

net from sequence [i] based on digital (45, 241)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 45 and N(F) ≥ 242, using
  - a curve from the manYPoints database [i]

(45, 111, 9832)-Net in Base 16 — Upper bound on s

There is no (45, 111, 9833)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 441758 043021 615856 111500 950809 258331 650925 856448 760704 933695 026119 197004 584663 067411 075067 591733 201976 476327 374689 385819 782169 634136 > 16¹¹¹ [i]