MinT - Information on Result #1185492

Information on Result #1185492

Digital (162, 191, 4218)-net over F₃, using net defined by OOA based on linear OOA(3¹⁹¹, 4218, F₃, 29, 29) (dual of [(4218, 29), 122131, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(3¹⁹¹, 59053, F₃, 29) (dual of [59053, 58862, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁹¹, 59059, F₃, 29) (dual of [59059, 58868, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
    1. linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 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, 192, 4218)-net over F₃	[i]	Net Duplication
2	Digital (164, 193, 4218)-net over F₃	[i]
3	Digital (165, 194, 4218)-net over F₃	[i]
4	Digital (176, 205, 4222)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (177, 206, 4225)-net over F₃	[i]
6	Digital (178, 207, 4226)-net over F₃	[i]
7	Digital (179, 208, 4228)-net over F₃	[i]
8	Digital (180, 209, 4230)-net over F₃	[i]