MinT - Best Known (40, 40+89, s)-Nets in Base 16

Best Known (40, 40+89, s)-Nets in Base 16

(40, 40+89, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 129, 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+89, 3637)-Net in Base 16 — Upper bound on s

There is no (40, 129, 3638)-net in base 16, because

1 times m-reduction [i] would yield (40, 128, 3638)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13460 890743 862025 827614 098575 955918 433794 144651 950449 476604 425825 569691 610701 031287 462085 686812 960893 538522 910831 303010 155250 903895 913533 065409 478672 609806 > 16¹²⁸ [i]