MinT - Information on Result #1208246

Information on Result #1208246

Digital (165, 179, 1366573)-net over F₃, using (u,Â u+v)-construction based on

digital (2, 9, 9)-net over F₃, using
- a shift-net [i]
digital (156, 170, 1366564)-net over F₃, using
- trace code for nets [i] based on digital (71, 85, 683282)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁸⁵, 683282, F₉, 14, 14) (dual of [(683282, 14), 9565863, 15]-NRT-code), using
    - OA 7-folding and stacking [i] based on linear OA(9⁸⁵, 4782974, F₉, 14) (dual of [4782974, 4782889, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁸⁵, 4782976, F₉, 14) (dual of [4782976, 4782891, 15]-code), using
        constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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: 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.