MinT - Best Known (40, 113, s)-Nets in Base 16

Best Known (40, 113, s)-Nets in Base 16

(40, 113, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 113, 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, 113, 5286)-Net in Base 16 — Upper bound on s

There is no (40, 113, 5287)-net in base 16, because

1 times m-reduction [i] would yield (40, 112, 5287)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 729 403696 779970 779616 593576 210756 194493 605050 119840 493994 320836 396444 661462 626894 770217 485308 438966 453835 160873 493598 558702 281245 707731 > 16¹¹² [i]