MinT - Best Known (50, 50+41, s)-Nets in Base 5

Best Known (50, 50+41, s)-Nets in Base 5

(50, 50+41, 132)-Net over F₅ — Constructive and digital

Digital (50, 91, 132)-net over F₅, using

1 times m-reduction [i] based on digital (50, 92, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 46, 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]

(50, 50+41, 139)-Net over F₅ — Digital

Digital (50, 91, 139)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+41, 2886)-Net in Base 5 — Upper bound on s

There is no (50, 91, 2887)-net in base 5, because

1 times m-reduction [i] would yield (50, 90, 2887)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 808 069069 876051 303432 660424 608396 626885 046463 081719 102264 911025 > 5⁹⁰ [i]