MinT - Best Known (40, 107, s)-Nets in Base 16

Best Known (40, 107, s)-Nets in Base 16

(40, 107, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 107, 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, 107, 6453)-Net in Base 16 — Upper bound on s

There is no (40, 107, 6454)-net in base 16, because

1 times m-reduction [i] would yield (40, 106, 6454)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 352204 821685 103049 893464 798543 669444 885012 224044 222603 236784 675124 570353 405792 712296 565234 036797 643436 233854 572123 035321 588981 > 16¹⁰⁶ [i]