MinT - Information on Result #1767564

Information on Result #1767564

Digital (172, 196, 166896)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁶, 166896, F₃, 3, 24) (dual of [(166896, 3), 500492, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹⁶, 177156, F₃, 3, 24) (dual of [(177156, 3), 531272, 25]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁹⁵, 177156, F₃, 3, 24) (dual of [(177156, 3), 531273, 25]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁹⁵, 531468, F₃, 24) (dual of [531468, 531273, 25]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹⁹⁴, 531467, F₃, 24) (dual of [531467, 531273, 25]-code), using
      - constructionÂ X4 applied to C_e(24) âŠ‚ C_e(21) [i] based on
        linear OA(3¹⁹³, 531441, F₃, 25) (dual of [531441, 531248, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(3²⁵, 26, F₃, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
        dual of repetition code with length 26 [i]
        linear OA(3¹, 26, F₃, 1) (dual of [26, 25, 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.