MinT - Best Known (23, 23+20, s)-Nets in Base 5

Best Known (23, 23+20, s)-Nets in Base 5

(23, 23+20, 54)-Net over F₅ — Constructive and digital

Digital (23, 43, 54)-net over F₅, using

1 times m-reduction [i] based on digital (23, 44, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 22, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(23, 23+20, 72)-Net over F₅ — Digital

Digital (23, 43, 72)-net over F₅, using

1 times m-reduction [i] based on digital (23, 44, 72)-net over F₅, using
- trace code for nets [i] based on digital (1, 22, 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]

(23, 23+20, 1139)-Net in Base 5 — Upper bound on s

There is no (23, 43, 1140)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 138704 876952 595908 967912 728001 > 5⁴³ [i]