MinT - Best Known (20, 37, s)-Nets in Base 5

Best Known (20, 37, s)-Nets in Base 5

(20, 37, 54)-Net over F₅ — Constructive and digital

Digital (20, 37, 54)-net over F₅, using

1 times m-reduction [i] based on digital (20, 38, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 19, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(20, 37, 72)-Net over F₅ — Digital

Digital (20, 37, 72)-net over F₅, using

1 times m-reduction [i] based on digital (20, 38, 72)-net over F₅, using
- trace code for nets [i] based on digital (1, 19, 36)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 35)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(20, 37, 1309)-Net in Base 5 — Upper bound on s

There is no (20, 37, 1310)-net in base 5, because

1 times m-reduction [i] would yield (20, 36, 1310)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 576841 414967 769386 942849 > 5³⁶ [i]