MinT - Best Known (63−25, 63, s)-Nets in Base 5

Best Known (63−25, 63, s)-Nets in Base 5

(63−25, 63, 132)-Net over F₅ — Constructive and digital

Digital (38, 63, 132)-net over F₅, using

5 times m-reduction [i] based on digital (38, 68, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 34, 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]

(63−25, 63, 168)-Net over F₅ — Digital

Digital (38, 63, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−25, 63, 5394)-Net in Base 5 — Upper bound on s

There is no (38, 63, 5395)-net in base 5, because

1 times m-reduction [i] would yield (38, 62, 5395)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 21 701015 643258 750014 630980 066833 826725 023313 > 5⁶² [i]