MinT - Best Known (18, 33, s)-Nets in Base 5

Best Known (18, 33, s)-Nets in Base 5

(18, 33, 54)-Net over F₅ — Constructive and digital

Digital (18, 33, 54)-net over F₅, using

1 times m-reduction [i] based on digital (18, 34, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 17, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(18, 33, 72)-Net over F₅ — Digital

Digital (18, 33, 72)-net over F₅, using

1 times m-reduction [i] based on digital (18, 34, 72)-net over F₅, using
- trace code for nets [i] based on digital (1, 17, 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]

(18, 33, 1320)-Net in Base 5 — Upper bound on s

There is no (18, 33, 1321)-net in base 5, because

1 times m-reduction [i] would yield (18, 32, 1321)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 23399 472357 502195 446605 > 5³² [i]