MinT - Information on Result #1185128

Information on Result #1185128

Digital (188, 211, 434816)-net over F₃, using net defined by OOA based on linear OOA(3²¹¹, 434816, F₃, 23, 23) (dual of [(434816, 23), 10000557, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(3²¹¹, 4782977, F₃, 23) (dual of [4782977, 4782766, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3²¹¹, 4782983, F₃, 23) (dual of [4782983, 4782772, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
    1. linear OA(3²¹¹, 4782969, F₃, 23) (dual of [4782969, 4782758, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(3¹⁹⁷, 4782969, F₃, 22) (dual of [4782969, 4782772, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 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 (189, 212, 434816)-net over F₃	[i]	Net Duplication
2	Digital (190, 213, 434816)-net over F₃	[i]
3	Digital (191, 214, 434816)-net over F₃	[i]
4	Digital (200, 223, 434823)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
5	Digital (201, 224, 434824)-net over F₃	[i]
6	Digital (202, 225, 434826)-net over F₃	[i]