MinT - Information on Result #1771728

Information on Result #1771728

Digital (216, 243, 448809)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴³, 448809, F₃, 3, 27) (dual of [(448809, 3), 1346184, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴³, 531456, F₃, 3, 27) (dual of [(531456, 3), 1594125, 28]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3²⁴⁴, 531457, F₃, 3, 28) (dual of [(531457, 3), 1594127, 29]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁴⁴, 1594371, F₃, 28) (dual of [1594371, 1594127, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(22) [i] based on
      1. linear OA(3²³⁵, 1594323, F₃, 28) (dual of [1594323, 1594088, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(3¹⁹⁶, 1594323, F₃, 23) (dual of [1594323, 1594127, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3⁹, 48, F₃, 4) (dual of [48, 39, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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.