MinT - Best Known (40, 40+86, s)-Nets in Base 16

Best Known (40, 40+86, s)-Nets in Base 16

(40, 40+86, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 126, 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+86, 3775)-Net in Base 16 — Upper bound on s

There is no (40, 126, 3776)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 557482 694441 609487 181103 842485 581746 166108 950541 642754 632099 214034 583078 780606 484671 050248 968455 007126 733682 389970 196848 334868 052988 185766 553508 957071 > 16¹²⁶ [i]