MinT - Best Known (42, 42+86, s)-Nets in Base 16

Best Known (42, 42+86, s)-Nets in Base 16

(42, 42+86, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 128, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 128, 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]

(42, 42+86, 4298)-Net in Base 16 — Upper bound on s

There is no (42, 128, 4299)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13453 203684 311285 707295 300120 058347 551516 816419 037457 824155 954376 957518 465849 166993 677206 103986 844135 588705 146543 403474 595808 790617 549436 066966 869327 277856 > 16¹²⁸ [i]