MinT - Best Known (40, 40+85, s)-Nets in Base 16

Best Known (40, 40+85, s)-Nets in Base 16

(40, 40+85, 225)-Net over F₁₆ — Constructive and digital

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]

(40, 40+85, 3927)-Net in Base 16 — Upper bound on s

There is no (40, 125, 3928)-net in base 16, because

1 times m-reduction [i] would yield (40, 124, 3928)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 204681 113438 837128 779413 787177 700872 739977 015689 628288 475535 488256 627555 615429 939826 376159 604371 396947 957407 359149 867094 684589 083245 106350 962186 795116 > 16¹²⁴ [i]