MinT - Information on Result #1187864

Information on Result #1187864

Digital (190, 223, 16386)-net over F₄, using net defined by OOA based on linear OOA(4²²³, 16386, F₄, 33, 33) (dual of [(16386, 33), 540515, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(4²²³, 262177, F₄, 33) (dual of [262177, 261954, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²²², 262176, F₄, 33) (dual of [262176, 261954, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [i] based on
    1. linear OA(4²¹⁷, 262144, F₄, 33) (dual of [262144, 261927, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(4⁵, 32, F₄, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
      - discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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 (191, 223, 16386)-net over F₄	[i]	t-Expansion
2	Digital (191, 224, 16386)-net over F₄	[i]	Net Duplication
3	Digital (192, 225, 16386)-net over F₄	[i]
4	Digital (193, 226, 16386)-net over F₄	[i]
5	Digital (194, 227, 16386)-net over F₄	[i]
6	Digital (195, 228, 16386)-net over F₄	[i]