MinT - Information on Result #1766796

Information on Result #1766796

Digital (165, 186, 490875)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁶, 490875, F₃, 3, 21) (dual of [(490875, 3), 1472439, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁶, 531451, F₃, 3, 21) (dual of [(531451, 3), 1594167, 22]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁸⁵, 531451, F₃, 3, 21) (dual of [(531451, 3), 1594168, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁸⁵, 1594353, F₃, 21) (dual of [1594353, 1594168, 22]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹⁸⁴, 1594352, F₃, 21) (dual of [1594352, 1594168, 22]-code), using
      - constructionÂ X4 applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
        linear OA(3¹⁸³, 1594324, F₃, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(3¹⁵⁷, 1594324, F₃, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
        linear OA(3²⁷, 28, F₃, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
        dual of repetition code with length 28 [i]
        linear OA(3¹, 28, F₃, 1) (dual of [28, 27, 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.