MinT - Best Known (45, 45+82, s)-Nets in Base 16

Best Known (45, 45+82, s)-Nets in Base 16

(45, 45+82, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 127, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 127, 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, 45+82, 242)-Net over F₁₆ — Digital

Digital (45, 127, 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, 45+82, 5753)-Net in Base 16 — Upper bound on s

There is no (45, 127, 5754)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 839 884238 056723 671372 256230 952504 360520 820566 296117 150799 306438 050062 799434 174766 057278 605749 096124 722088 434094 008478 616836 062586 185253 722944 578003 289961 > 16¹²⁷ [i]