MinT - Best Known (90−70, 90, s)-Nets in Base 16

Best Known (90−70, 90, s)-Nets in Base 16

(90−70, 90, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 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]

(90−70, 90, 129)-Net over F₁₆ — Digital

Digital (20, 90, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 90, 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]

(90−70, 90, 1138)-Net in Base 16 — Upper bound on s

There is no (20, 90, 1139)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 410369 842484 706337 943969 751813 427321 063020 300224 591965 815421 616989 068516 306735 417002 736598 926580 064612 182976 > 16⁹⁰ [i]