MinT - Best Known (26−14, 26, s)-Nets in Base 7

Best Known (26−14, 26, s)-Nets in Base 7

(26−14, 26, 25)-Net over F₇ — Constructive and digital

Digital (12, 26, 25)-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 (1, 15, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]

(26−14, 26, 46)-Net over F₇ — Digital

Digital (12, 26, 46)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(26−14, 26, 771)-Net in Base 7 — Upper bound on s

There is no (12, 26, 772)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 9425 024528 330167 359073 > 7²⁶ [i]