MinT - Best Known (26−12, 26, s)-Nets in Base 5

Best Known (26−12, 26, s)-Nets in Base 5

(26−12, 26, 54)-Net over F₅ — Constructive and digital

Digital (14, 26, 54)-net over F₅, using

trace code for nets [i] based on digital (1, 13, 27)-net over F₂₅, using
- net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
  - Niederreiter sequence [i]

(26−12, 26, 72)-Net over F₅ — Digital

Digital (14, 26, 72)-net over F₅, using

trace code for nets [i] based on digital (1, 13, 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]

(26−12, 26, 795)-Net in Base 5 — Upper bound on s

There is no (14, 26, 796)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 491222 328448 524865 > 5²⁶ [i]