MinT - Best Known (59−26, 59, s)-Nets in Base 5

Best Known (59−26, 59, s)-Nets in Base 5

(59−26, 59, 104)-Net over F₅ — Constructive and digital

Digital (33, 59, 104)-net over F₅, using

1 times m-reduction [i] based on digital (33, 60, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 30, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(59−26, 59, 112)-Net over F₅ — Digital

Digital (33, 59, 112)-net over F₅, using

1 times m-reduction [i] based on digital (33, 60, 112)-net over F₅, using
- trace code for nets [i] based on digital (3, 30, 56)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 55)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 56, using
      - fields by Serre with genus 3 or 4 [i]

(59−26, 59, 2097)-Net in Base 5 — Upper bound on s

There is no (33, 59, 2098)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 174087 894300 363791 298326 122607 291039 302345 > 5⁵⁹ [i]