MinT - Information on Result #1187562

Information on Result #1187562

Digital (194, 221, 322639)-net over F₄, using net defined by OOA based on linear OOA(4²²¹, 322639, F₄, 27, 27) (dual of [(322639, 27), 8711032, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(4²²¹, 4194308, F₄, 27) (dual of [4194308, 4194087, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4²²¹, 4194315, F₄, 27) (dual of [4194315, 4194094, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
    1. linear OA(4²²¹, 4194304, F₄, 27) (dual of [4194304, 4194083, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(4²¹⁰, 4194304, F₄, 26) (dual of [4194304, 4194094, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(4⁰, 11, F₄, 0) (dual of [11, 11, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (207, 234, 322644)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
2	Digital (208, 235, 322648)-net over F₄	[i]
3	Digital (209, 236, 322649)-net over F₄	[i]
4	Digital (210, 237, 322653)-net over F₄	[i]
5	Digital (211, 238, 322654)-net over F₄	[i]
6	Digital (212, 239, 322656)-net over F₄	[i]