MinT - Information on Result #1186348

Information on Result #1186348

Digital (114, 127, 1398197)-net over F₄, using net defined by OOA based on linear OOA(4¹²⁷, 1398197, F₄, 15, 13) (dual of [(1398197, 15), 20972828, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(4¹²⁷, 2796395, F₄, 3, 13) (dual of [(2796395, 3), 8389058, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹²⁷, 2796396, F₄, 3, 13) (dual of [(2796396, 3), 8389061, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹⁸, 195, F₄, 3, 6) (dual of [(195, 3), 567, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 18, 195)-net over F₄, using
        trace code for nets [i] based on digital (0, 6, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
    2. linear OOA(4¹⁰⁹, 2796201, F₄, 3, 13) (dual of [(2796201, 3), 8388494, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.