MinT - Best Known (50−16, 50, s)-Nets in Base 7

Best Known (50−16, 50, s)-Nets in Base 7

(50−16, 50, 202)-Net over F₇ — Constructive and digital

Digital (34, 50, 202)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (8, 16, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 8, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [i]
2. digital (18, 34, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 17, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(50−16, 50, 710)-Net over F₇ — Digital

Digital (34, 50, 710)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(50−16, 50, 120056)-Net in Base 7 — Upper bound on s

There is no (34, 50, 120057)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 798577 861183 739606 352890 009905 362191 893185 > 7⁵⁰ [i]