MinT - Information on Result #1715706

Information on Result #1715706

Digital (165, 192, 9774)-net over F₃, using net defined by OOA based on linear OOA(3¹⁹², 9774, F₃, 35, 27) (dual of [(9774, 35), 341898, 28]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(3¹⁹², 29323, F₃, 5, 27) (dual of [(29323, 5), 146423, 28]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁹², 29323, F₃, 2, 27) (dual of [(29323, 2), 58454, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁹², 29550, F₃, 2, 27) (dual of [(29550, 2), 58908, 28]-NRT-code), using
    - strength reduction [i] based on linear OOA(3¹⁹², 29550, F₃, 2, 28) (dual of [(29550, 2), 58908, 29]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(3¹⁹², 59100, F₃, 28) (dual of [59100, 58908, 29]-code), using
        constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [i] based on
        linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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.