MinT - Best Known (90−76, 90, s)-Nets in Base 16

Best Known (90−76, 90, s)-Nets in Base 16

(90−76, 90, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 90, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 90, 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]

(90−76, 90, 97)-Net over F₁₆ — Digital

Digital (14, 90, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 90, 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]

(90−76, 90, 691)-Net in Base 16 — Upper bound on s

There is no (14, 90, 692)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 441044 467350 396350 950702 942813 575734 371590 857500 078548 842604 025114 896551 182295 984908 586987 148156 612871 953716 > 16⁹⁰ [i]