MinT - Best Known (20, 35, s)-Nets in Base 16

Best Known (20, 35, s)-Nets in Base 16

(20, 35, 518)-Net over F₁₆ — Constructive and digital

Digital (20, 35, 518)-net over F₁₆, using

1 times m-reduction [i] based on 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, 35, 642)-Net over F₁₆ — Digital

Digital (20, 35, 642)-net over F₁₆, using

1 times m-reduction [i] based on 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, 35, 159001)-Net in Base 16 — Upper bound on s

There is no (20, 35, 159002)-net in base 16, because

1 times m-reduction [i] would yield (20, 34, 159002)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 87114 945046 055575 095393 630425 874954 925636 > 16³⁴ [i]