MinT - Information on Result #1208201

Information on Result #1208201

Digital (224, 237, 5612086)-net over F₃, using (u,Â u+v)-construction based on

digital (35, 41, 19686)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁴¹, 19686, F₃, 6, 6) (dual of [(19686, 6), 118075, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁴¹, 19686, F₃, 5, 6) (dual of [(19686, 5), 98389, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁴¹, 59058, F₃, 6) (dual of [59058, 59017, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴¹, 59060, F₃, 6) (dual of [59060, 59019, 7]-code), using
        1 times truncation [i] based on linear OA(3⁴², 59061, F₃, 7) (dual of [59061, 59019, 8]-code), using
        constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
        linear OA(3⁴¹, 59049, F₃, 7) (dual of [59049, 59008, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(3³¹, 59049, F₃, 5) (dual of [59049, 59018, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(3¹¹, 12, F₃, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
        dual of repetition code with length 12 [i]
        linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 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]
digital (183, 196, 5592400)-net over F₃, using
- trace code for nets [i] based on digital (85, 98, 2796200)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁹⁸, 2796200, F₉, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OOA(9⁹⁸, 8388601, F₉, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(9⁹⁸, 8388602, F₉, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
        trace code [i] based on linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.