MinT - Information on Result #1187866

Information on Result #1187866

Digital (196, 229, 16387)-net over F₄, using net defined by OOA based on linear OOA(4²²⁹, 16387, F₄, 33, 33) (dual of [(16387, 33), 540542, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(4²²⁹, 262193, F₄, 33) (dual of [262193, 261964, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4²²⁷, 262191, F₄, 33) (dual of [262191, 261964, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [i] based on
    1. linear OA(4²¹⁷, 262145, F₄, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    2. linear OA(4¹⁸¹, 262145, F₄, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    3. linear OA(4¹⁰, 46, F₄, 5) (dual of [46, 36, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Constructive and 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

The following results depend on this result:

	Result		Method
1	Digital (197, 229, 16387)-net over F₄	[i]	t-Expansion
2	Digital (197, 230, 16387)-net over F₄	[i]	Net Duplication
3	Digital (198, 231, 16387)-net over F₄	[i]
4	Digital (199, 232, 16387)-net over F₄	[i]
5	Digital (196, 228, 16387)-net over F₄	[i]	m-Reduction