MinT - Best Known (46, 46+27, s)-Nets in Base 5

Best Known (46, 46+27, s)-Nets in Base 5

(46, 46+27, 208)-Net over F₅ — Constructive and digital

Digital (46, 73, 208)-net over F₅, using

1 times m-reduction [i] based on digital (46, 74, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 37, 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]

(46, 46+27, 248)-Net over F₅ — Digital

Digital (46, 73, 248)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+27, 10524)-Net in Base 5 — Upper bound on s

There is no (46, 73, 10525)-net in base 5, because

1 times m-reduction [i] would yield (46, 72, 10525)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 212 004483 993168 444008 215482 163185 921580 159302 904581 > 5⁷² [i]