MinT - Best Known (86−37, 86, s)-Nets in Base 5

Best Known (86−37, 86, s)-Nets in Base 5

(86−37, 86, 132)-Net over F₅ — Constructive and digital

Digital (49, 86, 132)-net over F₅, using

4 times m-reduction [i] based on digital (49, 90, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 45, 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]

(86−37, 86, 156)-Net over F₅ — Digital

Digital (49, 86, 156)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−37, 86, 3760)-Net in Base 5 — Upper bound on s

There is no (49, 86, 3761)-net in base 5, because

1 times m-reduction [i] would yield (49, 85, 3761)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 258904 366711 375232 466825 666637 338981 458895 542472 619127 025625 > 5⁸⁵ [i]