MinT - Best Known (40, 40+82, s)-Nets in Base 16

Best Known (40, 40+82, s)-Nets in Base 16

(40, 40+82, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 122, 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]

(40, 40+82, 4096)-Net in Base 16 — Upper bound on s

There is no (40, 122, 4097)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 803 177660 870816 676090 745413 651103 365150 336619 411115 931242 024767 826383 963790 447571 398009 103195 676467 370218 155900 632424 554886 921981 332936 002006 470656 > 16¹²² [i]