MinT - Best Known (119−96, 119, s)-Nets in Base 16

Best Known (119−96, 119, s)-Nets in Base 16

(119−96, 119, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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]

(119−96, 119, 129)-Net over F₁₆ — Digital

Digital (23, 119, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 119, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(119−96, 119, 1181)-Net in Base 16 — Upper bound on s

There is no (23, 119, 1182)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 202890 931323 528342 470840 916665 044577 015525 343165 914891 515581 839981 551132 711585 451697 192376 014801 788629 522404 602551 475901 815293 048896 782529 120316 > 16¹¹⁹ [i]