MinT - Best Known (50, 50+31, s)-Nets in Base 5

Best Known (50, 50+31, s)-Nets in Base 5

(50, 50+31, 208)-Net over F₅ — Constructive and digital

Digital (50, 81, 208)-net over F₅, using

1 times m-reduction [i] based on digital (50, 82, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 41, 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]

(50, 50+31, 231)-Net over F₅ — Digital

Digital (50, 81, 231)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+31, 8570)-Net in Base 5 — Upper bound on s

There is no (50, 81, 8571)-net in base 5, because

1 times m-reduction [i] would yield (50, 80, 8571)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 82 800777 220295 327930 203500 233466 040268 914598 176446 351861 > 5⁸⁰ [i]