MinT - Best Known (38−12, 38, s)-Nets in Base 7

Best Known (38−12, 38, s)-Nets in Base 7

(38−12, 38, 202)-Net over F₇ — Constructive and digital

Digital (26, 38, 202)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 12, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 6, 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 (14, 26, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 13, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(38−12, 38, 685)-Net over F₇ — Digital

Digital (26, 38, 685)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(38−12, 38, 112290)-Net in Base 7 — Upper bound on s

There is no (26, 38, 112291)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 129 934930 804537 894995 047469 139045 > 7³⁸ [i]