MinT - Information on Result #1768808

Information on Result #1768808

Digital (186, 211, 360129)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹¹, 360129, F₃, 4, 25) (dual of [(360129, 4), 1440305, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹¹, 398584, F₃, 4, 25) (dual of [(398584, 4), 1594125, 26]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²¹⁰, 398584, F₃, 4, 25) (dual of [(398584, 4), 1594126, 26]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²¹⁰, 1594336, F₃, 25) (dual of [1594336, 1594126, 26]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹⁰, 1594337, F₃, 25) (dual of [1594337, 1594127, 26]-code), using
      - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
        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]
        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]
        linear OA(3¹, 14, F₃, 1) (dual of [14, 13, 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]

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.