MinT - Information on Result #1185310

Information on Result #1185310

Digital (162, 188, 13627)-net over F₃, using net defined by OOA based on linear OOA(3¹⁸⁸, 13627, F₃, 26, 26) (dual of [(13627, 26), 354114, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(3¹⁸⁸, 177151, F₃, 26) (dual of [177151, 176963, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁸⁸, 177158, F₃, 26) (dual of [177158, 176970, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(3¹⁸⁸, 177147, F₃, 26) (dual of [177147, 176959, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3¹⁷⁷, 177147, F₃, 25) (dual of [177147, 176970, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 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: 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 (163, 189, 13627)-net over F₃	[i]	Net Duplication
2	Digital (164, 190, 13627)-net over F₃	[i]
3	Digital (165, 191, 13627)-net over F₃	[i]
4	Digital (176, 202, 13634)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (177, 203, 13635)-net over F₃	[i]
6	Digital (178, 204, 13637)-net over F₃	[i]