MinT - Best Known (45, 45+60, s)-Nets in Base 16

Best Known (45, 45+60, s)-Nets in Base 16

(45, 45+60, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 105, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 105, 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+60, 242)-Net over F₁₆ — Digital

Digital (45, 105, 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+60, 13139)-Net in Base 16 — Upper bound on s

There is no (45, 105, 13140)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 711962 329422 292595 391387 642419 339238 539989 780498 843405 707564 432176 935995 968077 601819 675051 162008 483047 011472 043752 793923 667376 > 16¹⁰⁵ [i]