MinT - Information on Result #1205098

Information on Result #1205098

Digital (171, 182, 5592482)-net over F₃, using trace code for nets based on digital (80, 91, 2796241)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁹¹, 2796241, F₉, 15, 11) (dual of [(2796241, 15), 41943524, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁹¹, 5592483, F₉, 3, 11) (dual of [(5592483, 3), 16777358, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁹¹, 5592484, F₉, 3, 11) (dual of [(5592484, 3), 16777361, 12]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁹, 82, F₉, 3, 5) (dual of [(82, 3), 237, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 9, 82)-net over F₉, using
        base reduction for projective spaces (embedding PG(4,81) in PG(8,9)) for nets [i] based on digital (0, 5, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
      2. linear OOA(9⁸², 5592402, F₉, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
        trace code [i] based on linear OOA(81⁴¹, 2796201, F₈₁, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.