MinT - Best Known (20, 36, s)-Nets in Base 16

Best Known (20, 36, s)-Nets in Base 16

(20, 36, 518)-Net over F₁₆ — Constructive and digital

Digital (20, 36, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 18, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(20, 36, 642)-Net over F₁₆ — Digital

Digital (20, 36, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 18, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(20, 36, 65782)-Net in Base 16 — Upper bound on s

There is no (20, 36, 65783)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 22 301391 609128 932636 829986 660386 122349 348886 > 16³⁶ [i]