MinT - Best Known (26−11, 26, s)-Nets in Base 5

Best Known (26−11, 26, s)-Nets in Base 5

(26−11, 26, 56)-Net over F₅ — Constructive and digital

Digital (15, 26, 56)-net over F₅, using

trace code for nets [i] based on digital (2, 13, 28)-net over F₂₅, using
- net from sequence [i] based on digital (2, 27)-sequence over F₂₅, using
  - Niederreiter sequence [i]

(26−11, 26, 92)-Net over F₅ — Digital

Digital (15, 26, 92)-net over F₅, using

trace code for nets [i] based on digital (2, 13, 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]

(26−11, 26, 2032)-Net in Base 5 — Upper bound on s

There is no (15, 26, 2033)-net in base 5, because

1 times m-reduction [i] would yield (15, 25, 2033)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 298725 322091 637749 > 5²⁵ [i]