MinT - Information on Result #1765867

Information on Result #1765867

Digital (153, 173, 398938)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷³, 398938, F₃, 3, 20) (dual of [(398938, 3), 1196641, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷³, 531446, F₃, 3, 20) (dual of [(531446, 3), 1594165, 21]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁷², 531446, F₃, 3, 20) (dual of [(531446, 3), 1594166, 21]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁷², 1594338, F₃, 20) (dual of [1594338, 1594166, 21]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(3¹⁷⁰, 1594336, F₃, 20) (dual of [1594336, 1594166, 21]-code), using
      - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
        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(3¹⁵⁷, 1594323, F₃, 19) (dual of [1594323, 1594166, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(3⁰, 13, F₃, 0) (dual of [13, 13, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.