MinT - Information on Result #1766577

Information on Result #1766577

Digital (162, 183, 404362)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸³, 404362, F₃, 3, 21) (dual of [(404362, 3), 1212903, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸³, 531445, F₃, 3, 21) (dual of [(531445, 3), 1594152, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁸³, 1594335, F₃, 21) (dual of [1594335, 1594152, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸³, 1594336, F₃, 21) (dual of [1594336, 1594153, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁸⁴, 1594337, F₃, 22) (dual of [1594337, 1594153, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [i] based on
        linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        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]
        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.