MinT - Best Known (96−82, 96, s)-Nets in Base 16

Best Known (96−82, 96, s)-Nets in Base 16

(96−82, 96, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 96, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 96, 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]

(96−82, 96, 97)-Net over F₁₆ — Digital

Digital (14, 96, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 96, 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]

(96−82, 96, 687)-Net in Base 16 — Upper bound on s

There is no (14, 96, 688)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 40 813476 044189 476407 532595 950489 048404 023936 810868 568739 255856 415263 392208 231879 123397 182069 976743 793460 109155 643871 > 16⁹⁶ [i]