MinT - Best Known (41, 41+89, s)-Nets in Base 16

Best Known (41, 41+89, s)-Nets in Base 16

(41, 41+89, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 130, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 130, 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]

(41, 41+89, 3875)-Net in Base 16 — Upper bound on s

There is no (41, 130, 3876)-net in base 16, because

1 times m-reduction [i] would yield (41, 129, 3876)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 214880 216140 380691 956944 202255 302694 762868 859647 725506 470988 139811 147450 468291 267251 216347 273017 521382 567755 575761 567318 844969 598775 007119 234917 480319 395136 > 16¹²⁹ [i]