MinT - Best Known (45, 45+78, s)-Nets in Base 16

Best Known (45, 45+78, s)-Nets in Base 16

(45, 45+78, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 123, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 123, 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+78, 242)-Net over F₁₆ — Digital

Digital (45, 123, 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+78, 6419)-Net in Base 16 — Upper bound on s

There is no (45, 123, 6420)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12843 491037 519222 548864 533658 849990 244126 079910 159653 144287 985704 516129 298142 471223 883529 954390 619402 104209 238586 634167 715130 488610 028533 340782 668576 > 16¹²³ [i]