MinT - Best Known (40, 116, s)-Nets in Base 16

Best Known (40, 116, s)-Nets in Base 16

(40, 116, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 116, 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, 116, 4726)-Net in Base 16 — Upper bound on s

There is no (40, 116, 4727)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 905978 879698 800608 608022 115264 232546 886093 553528 724134 531547 630226 284191 741541 286001 687287 238829 025394 106887 519042 742427 761617 499998 220541 > 16¹¹⁶ [i]