MinT - Best Known (77−32, 77, s)-Nets in Base 5

Best Known (77−32, 77, s)-Nets in Base 5

(77−32, 77, 132)-Net over F₅ — Constructive and digital

Digital (45, 77, 132)-net over F₅, using

5 times m-reduction [i] based on digital (45, 82, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 41, 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]

(77−32, 77, 162)-Net over F₅ — Digital

Digital (45, 77, 162)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−32, 77, 3917)-Net in Base 5 — Upper bound on s

There is no (45, 77, 3918)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 663308 144704 015782 036288 654778 730809 554953 538935 662337 > 5⁷⁷ [i]