MinT - Best Known (45, 45+80, s)-Nets in Base 16

Best Known (45, 45+80, s)-Nets in Base 16

(45, 45+80, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 125, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 125, 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+80, 242)-Net over F₁₆ — Digital

Digital (45, 125, 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+80, 6067)-Net in Base 16 — Upper bound on s

There is no (45, 125, 6068)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 289389 396572 475376 798029 566894 514079 586877 347302 155577 960218 882506 226013 774170 418453 204164 840103 007738 612662 331366 981724 278392 262069 659797 051285 979426 > 16¹²⁵ [i]