MinT - Best Known (92−47, 92, s)-Nets in Base 16

Best Known (92−47, 92, s)-Nets in Base 16

(92−47, 92, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 92, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 92, 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]

(92−47, 92, 301)-Net over F₁₆ — Digital

Digital (45, 92, 301)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−47, 92, 36504)-Net in Base 16 — Upper bound on s

There is no (45, 92, 36505)-net in base 16, because

1 times m-reduction [i] would yield (45, 91, 36505)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 595617 348318 162661 837558 927593 774266 553494 064768 584349 357879 973601 872070 072111 555868 018953 759121 122150 159976 > 16⁹¹ [i]