MinT - Best Known (18, 18+17, s)-Nets in Base 7

Best Known (18, 18+17, s)-Nets in Base 7

(18, 18+17, 100)-Net over F₇ — Constructive and digital

Digital (18, 35, 100)-net over F₇, using

1 times m-reduction [i] based on digital (18, 36, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 18, 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]

(18, 18+17, 2445)-Net in Base 7 — Upper bound on s

There is no (18, 35, 2446)-net in base 7, because

1 times m-reduction [i] would yield (18, 34, 2446)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54224 435954 398206 810762 720913 > 7³⁴ [i]