MinT - Best Known (45, 45+22, s)-Nets in Base 7

Best Known (45, 45+22, s)-Nets in Base 7

(45, 45+22, 200)-Net over F₇ — Constructive and digital

Digital (45, 67, 200)-net over F₇, using

1 times m-reduction [i] based on digital (45, 68, 200)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 22, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 11, 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, 46, 100)-net over F₇, using
    - trace code for nets [i] based on digital (0, 23, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(45, 45+22, 729)-Net over F₇ — Digital

Digital (45, 67, 729)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+22, 114882)-Net in Base 7 — Upper bound on s

There is no (45, 67, 114883)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 418 413438 028961 526503 231119 697995 414626 172635 000429 390847 > 7⁶⁷ [i]