MinT - Information on Result #1766350

Information on Result #1766350

Digital (144, 180, 2168)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁸⁰, 2168, F₃, 36) (dual of [2168, 1988, 37]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, 2227, F₃, 36) (dual of [2227, 2047, 37]-code), using
- strength reduction [i] based on linear OA(3¹⁸⁰, 2227, F₃, 37) (dual of [2227, 2047, 38]-code), using
  - constructionÂ X applied to C([0,18]) âŠ‚ C([0,15]) [i] based on
    1. linear OA(3¹⁶⁹, 2188, F₃, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    2. linear OA(3¹⁴¹, 2188, F₃, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    3. linear OA(3¹¹, 39, F₃, 5) (dual of [39, 28, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 40, F₃, 5) (dual of [40, 29, 6]-code), using
        (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁷, 14, F₃, 5) (dual of [14, 7, 6]-code), using
        extended quadratic residue code Q_e(14,3) [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.