MinT - Best Known (109−45, 109, s)-Nets in Base 5

Best Known (109−45, 109, s)-Nets in Base 5

(109−45, 109, 208)-Net over F₅ — Constructive and digital

Digital (64, 109, 208)-net over F₅, using

1 times m-reduction [i] based on digital (64, 110, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 55, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(109−45, 109, 218)-Net over F₅ — Digital

Digital (64, 109, 218)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−45, 109, 6094)-Net in Base 5 — Upper bound on s

There is no (64, 109, 6095)-net in base 5, because

1 times m-reduction [i] would yield (64, 108, 6095)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3083 187032 252128 934868 767958 618133 126395 461832 129634 575825 485171 717823 862185 > 5¹⁰⁸ [i]