MinT - Best Known (56−26, 56, s)-Nets in Base 5

Best Known (56−26, 56, s)-Nets in Base 5

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

Digital (30, 56, 56)-net over F₅, using

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

(56−26, 56, 92)-Net over F₅ — Digital

Digital (30, 56, 92)-net over F₅, using

trace code for nets [i] based on digital (2, 28, 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]

(56−26, 56, 1443)-Net in Base 5 — Upper bound on s

There is no (30, 56, 1444)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1389 441450 544601 765730 264227 789996 235537 > 5⁵⁶ [i]