MinT - Best Known (56−22, 56, s)-Nets in Base 5

Best Known (56−22, 56, s)-Nets in Base 5

(56−22, 56, 132)-Net over F₅ — Constructive and digital

Digital (34, 56, 132)-net over F₅, using

4 times m-reduction [i] based on digital (34, 60, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 30, 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]

(56−22, 56, 162)-Net over F₅ — Digital

Digital (34, 56, 162)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−22, 56, 4431)-Net in Base 5 — Upper bound on s

There is no (34, 56, 4432)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1388 169468 980833 421911 621387 291721 230145 > 5⁵⁶ [i]