MinT - Best Known (40, 40+78, s)-Nets in Base 16

Best Known (40, 40+78, s)-Nets in Base 16

(40, 40+78, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 118, 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+78, 4492)-Net in Base 16 — Upper bound on s

There is no (40, 118, 4493)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12246 995345 615749 256851 571625 989489 191528 847233 452837 379982 221804 851085 610877 204582 040776 077954 793719 344563 801591 701741 019848 598678 284693 460256 > 16¹¹⁸ [i]