MinT - Best Known (25−14, 25, s)-Nets in Base 7

Best Known (25−14, 25, s)-Nets in Base 7

(25−14, 25, 24)-Net over F₇ — Constructive and digital

Digital (11, 25, 24)-net over F₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 4, 8)-net over F₇, using
  - net from sequence [i] based on digital (0, 7)-sequence over F₇, using
    - Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
      - the rational function field F₇(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 7, 8)-net over F₇, using
  - net from sequence [i] based on digital (0, 7)-sequence over F₇ (see above)
3. digital (0, 14, 8)-net over F₇, using
  - net from sequence [i] based on digital (0, 7)-sequence over F₇ (see above)

(25−14, 25, 39)-Net over F₇ — Digital

Digital (11, 25, 39)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(25−14, 25, 583)-Net in Base 7 — Upper bound on s

There is no (11, 25, 584)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1352 314629 434750 028097 > 7²⁵ [i]