MinT - Information on Result #1761748

Information on Result #1761748

Digital (73, 95, 708)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3⁹⁵, 708, F₃, 22) (dual of [708, 613, 23]-code), using

discarding factors / shortening the dual code based on linear OA(3⁹⁵, 763, F₃, 22) (dual of [763, 668, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
  1. linear OA(3⁸⁵, 729, F₃, 22) (dual of [729, 644, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(3⁶¹, 729, F₃, 16) (dual of [729, 668, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(3¹⁰, 34, F₃, 5) (dual of [34, 24, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
      - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        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]
        linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(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.