MinT - Information on Result #1799707

Information on Result #1799707

Digital (104, 125, 1062900)-net over F₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(9¹²⁵, 1062900, F₉, 21) (dual of [1062900, 1062775, 22]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(9¹²⁴, 1062898, F₉, 21) (dual of [1062898, 1062774, 22]-code), using
  - trace code [i] based on linear OA(81⁶², 531449, F₈₁, 21) (dual of [531449, 531387, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(81⁶¹, 531442, F₈₁, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(81⁵⁵, 531442, F₈₁, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(81¹, 7, F₈₁, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(9¹²⁴, 1062899, F₉, 20) (dual of [1062899, 1062775, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹²⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 3 774734 751311 834091 713400 248430 496415 461021 788445 208254 160849 911962 039544 766177 288727 188732 276098 082231 731123 599825 [i]
3. linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: 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.