MinT - Information on Result #1771726

Information on Result #1771726

Digital (213, 243, 133776)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴³, 133776, F₃, 3, 30) (dual of [(133776, 3), 401085, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴³, 177155, F₃, 3, 30) (dual of [(177155, 3), 531222, 31]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁴², 177155, F₃, 3, 30) (dual of [(177155, 3), 531223, 31]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁴², 531465, F₃, 30) (dual of [531465, 531223, 31]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁴², 531466, F₃, 30) (dual of [531466, 531224, 31]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
        linear OA(3²⁴¹, 531441, F₃, 31) (dual of [531441, 531200, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(3¹, 25, F₃, 1) (dual of [25, 24, 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.