MinT - Best Known (43, 43+20, s)-Nets in Base 7

Best Known (43, 43+20, s)-Nets in Base 7

(43, 43+20, 202)-Net over F₇ — Constructive and digital

Digital (43, 63, 202)-net over F₇, using

1 times m-reduction [i] based on digital (43, 64, 202)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 20, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 10, 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 (23, 44, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 22, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]

(43, 43+20, 847)-Net over F₇ — Digital

Digital (43, 63, 847)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+20, 159193)-Net in Base 7 — Upper bound on s

There is no (43, 63, 159194)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 174254 759654 725632 764712 249672 405943 510806 053203 955749 > 7⁶³ [i]