MinT - Best Known (19, 83, s)-Nets in Base 16

Best Known (19, 83, s)-Nets in Base 16

(19, 83, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 83, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 83, 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]

(19, 83, 129)-Net over F₁₆ — Digital

Digital (19, 83, 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]

(19, 83, 1114)-Net in Base 16 — Upper bound on s

There is no (19, 83, 1115)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8805 767536 130229 287872 569732 448370 772929 134193 111031 168070 618810 056290 146028 960815 659773 968239 372826 > 16⁸³ [i]