MinT - Best Known (112−72, 112, s)-Nets in Base 16

Best Known (112−72, 112, s)-Nets in Base 16

(112−72, 112, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 112, 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]

(112−72, 112, 5286)-Net in Base 16 — Upper bound on s

There is no (40, 112, 5287)-net in base 16, because

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]