MinT - Best Known (50, 50+43, s)-Nets in Base 5

Best Known (50, 50+43, s)-Nets in Base 5

(50, 50+43, 104)-Net over F₅ — Constructive and digital

Digital (50, 93, 104)-net over F₅, using

1 times m-reduction [i] based on digital (50, 94, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 47, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(50, 50+43, 128)-Net over F₅ — Digital

Digital (50, 93, 128)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+43, 2488)-Net in Base 5 — Upper bound on s

There is no (50, 93, 2489)-net in base 5, because

1 times m-reduction [i] would yield (50, 92, 2489)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20278 017630 622808 572069 483201 126174 077107 630630 052319 289790 120405 > 5⁹² [i]