MinT - Information on Result #1772425

Information on Result #1772425

Digital (222, 250, 398732)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁵⁰, 398732, F₃, 3, 28) (dual of [(398732, 3), 1195946, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁵⁰, 531463, F₃, 3, 28) (dual of [(531463, 3), 1594139, 29]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁴⁹, 531463, F₃, 3, 28) (dual of [(531463, 3), 1594140, 29]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁴⁶, 531462, F₃, 3, 28) (dual of [(531462, 3), 1594140, 29]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3²⁴⁶, 1594386, F₃, 28) (dual of [1594386, 1594140, 29]-code), using
      - constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [i] based on
        linear OA(3²³⁵, 1594323, F₃, 28) (dual of [1594323, 1594088, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        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(3¹¹, 63, F₃, 5) (dual of [63, 52, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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.