MinT - Best Known (48−22, 48, s)-Nets in Base 5

Best Known (48−22, 48, s)-Nets in Base 5

(48−22, 48, 56)-Net over F₅ — Constructive and digital

Digital (26, 48, 56)-net over F₅, using

trace code for nets [i] based on digital (2, 24, 28)-net over F₂₅, using
- net from sequence [i] based on digital (2, 27)-sequence over F₂₅, using
  - Niederreiter sequence [i]

(48−22, 48, 92)-Net over F₅ — Digital

Digital (26, 48, 92)-net over F₅, using

trace code for nets [i] based on digital (2, 24, 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]

(48−22, 48, 1369)-Net in Base 5 — Upper bound on s

There is no (26, 48, 1370)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3567 164218 326437 871070 187890 582793 > 5⁴⁸ [i]