MinT - Best Known (12, 22, s)-Nets in Base 5

Best Known (12, 22, s)-Nets in Base 5

(12, 22, 54)-Net over F₅ — Constructive and digital

Digital (12, 22, 54)-net over F₅, using

trace code for nets [i] based on digital (1, 11, 27)-net over F₂₅, using
- net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
  - Niederreiter sequence [i]

(12, 22, 72)-Net over F₅ — Digital

Digital (12, 22, 72)-net over F₅, using

trace code for nets [i] based on digital (1, 11, 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]

(12, 22, 771)-Net in Base 5 — Upper bound on s

There is no (12, 22, 772)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2389 531186 803601 > 5²² [i]