MinT - Best Known (45, 45+56, s)-Nets in Base 16

Best Known (45, 45+56, s)-Nets in Base 16

(45, 45+56, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 101, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 101, 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+56, 242)-Net over F₁₆ — Digital

Digital (45, 101, 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+56, 16593)-Net in Base 16 — Upper bound on s

There is no (45, 101, 16594)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 333087 079014 679972 097518 496630 828078 360495 642075 034966 026691 351382 463877 686796 841497 864343 635227 565362 584886 472667 915856 > 16¹⁰¹ [i]