MinT - Best Known (28, 51, s)-Nets in Base 5

Best Known (28, 51, s)-Nets in Base 5

(28, 51, 56)-Net over F₅ — Constructive and digital

Digital (28, 51, 56)-net over F₅, using

1 times m-reduction [i] based on digital (28, 52, 56)-net over F₅, using
- trace code for nets [i] based on digital (2, 26, 28)-net over F₂₅, using
  - net from sequence [i] based on digital (2, 27)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(28, 51, 92)-Net over F₅ — Digital

Digital (28, 51, 92)-net over F₅, using

1 times m-reduction [i] based on digital (28, 52, 92)-net over F₅, using
- trace code for nets [i] based on digital (2, 26, 46)-net over F₂₅, using
  - net from sequence [i] based on digital (2, 45)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 2 and N(F) ≥ 46, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(28, 51, 1837)-Net in Base 5 — Upper bound on s

There is no (28, 51, 1838)-net in base 5, because

1 times m-reduction [i] would yield (28, 50, 1838)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 88996 879663 779925 933918 929834 345433 > 5⁵⁰ [i]