MinT - Best Known (40, 40+55, s)-Nets in Base 16

Best Known (40, 40+55, s)-Nets in Base 16

(40, 40+55, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 95, 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+55, 11320)-Net in Base 16 — Upper bound on s

There is no (40, 95, 11321)-net in base 16, because

1 times m-reduction [i] would yield (40, 94, 11321)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 154058 222792 965723 023234 985941 955096 661514 534373 584770 102499 500507 860221 015685 921327 773635 042245 219033 526414 613856 > 16⁹⁴ [i]