MinT - Best Known (57−22, 57, s)-Nets in Base 5

Best Known (57−22, 57, s)-Nets in Base 5

(57−22, 57, 132)-Net over F₅ — Constructive and digital

Digital (35, 57, 132)-net over F₅, using

5 times m-reduction [i] based on digital (35, 62, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 31, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(57−22, 57, 177)-Net over F₅ — Digital

Digital (35, 57, 177)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−22, 57, 5131)-Net in Base 5 — Upper bound on s

There is no (35, 57, 5132)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6948 037027 293600 992855 771253 038261 573425 > 5⁵⁷ [i]