MinT - Information on Result #1769332

Information on Result #1769332

Digital (193, 217, 529003)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁷, 529003, F₃, 3, 24) (dual of [(529003, 3), 1586792, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁷, 531456, F₃, 3, 24) (dual of [(531456, 3), 1594151, 25]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3²¹⁸, 531457, F₃, 3, 25) (dual of [(531457, 3), 1594153, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²¹⁸, 1594371, F₃, 25) (dual of [1594371, 1594153, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
      1. linear OA(3²⁰⁹, 1594323, F₃, 25) (dual of [1594323, 1594114, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(3¹⁷⁰, 1594323, F₃, 20) (dual of [1594323, 1594153, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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.