MinT - Best Known (50−36, 50, s)-Nets in Base 16

Best Known (50−36, 50, s)-Nets in Base 16

(50−36, 50, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 50, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 50, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(50−36, 50, 97)-Net over F₁₆ — Digital

Digital (14, 50, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 50, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(50−36, 50, 1104)-Net in Base 16 — Upper bound on s

There is no (14, 50, 1105)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 629269 423189 379157 479402 896806 441528 908784 658375 786729 850976 > 16⁵⁰ [i]