MinT - Best Known (53, 53+26, s)-Nets in Base 7

Best Known (53, 53+26, s)-Nets in Base 7

(53, 53+26, 200)-Net over F₇ — Constructive and digital

Digital (53, 79, 200)-net over F₇, using

1 times m-reduction [i] based on digital (53, 80, 200)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 26, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 13, 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 (27, 54, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 27, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(53, 53+26, 807)-Net over F₇ — Digital

Digital (53, 79, 807)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+26, 129069)-Net in Base 7 — Upper bound on s

There is no (53, 79, 129070)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 791248 222197 777866 057609 014995 194781 326310 620544 162419 088588 357629 > 7⁷⁹ [i]