MinT - Information on Result #1189752

Information on Result #1189752

Digital (12, 19, 199)-net over F₇, using net defined by OOA based on linear OOA(7¹⁹, 199, F₇, 9, 7) (dual of [(199, 9), 1772, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(7¹⁹, 200, F₇, 3, 7) (dual of [(200, 3), 581, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁵, 132, F₇, 3, 3) (dual of [(132, 3), 391, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(7⁵, 132, F₇, 2, 3) (dual of [(132, 2), 259, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁵, 132, F₇, 3) (dual of [132, 127, 4]-code or 132-cap in PG(4,7)), using
        caps completed using a computer search [i]
  2. linear OOA(7¹⁴, 100, F₇, 3, 7) (dual of [(100, 3), 286, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 100)-net over F₇, using
      - trace code for nets [i] based on digital (0, 7, 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]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.