MinT - Best Known (51−25, 51, s)-Nets in Base 5

Best Known (51−25, 51, s)-Nets in Base 5

(51−25, 51, 52)-Net over F₅ — Constructive and digital

Digital (26, 51, 52)-net over F₅, using

1 times m-reduction [i] based on digital (26, 52, 52)-net over F₅, using
- trace code for nets [i] based on digital (0, 26, 26)-net over F₂₅, using
  - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
      - the rational function field F₂₅(x) [i]
    - Niederreiter sequence [i]

(51−25, 51, 68)-Net over F₅ — Digital

Digital (26, 51, 68)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−25, 51, 1072)-Net in Base 5 — Upper bound on s

There is no (26, 51, 1073)-net in base 5, because

1 times m-reduction [i] would yield (26, 50, 1073)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 89656 790652 751662 466762 268731 781201 > 5⁵⁰ [i]