MinT - Information on Result #1193814

Information on Result #1193814

Digital (71, 85, 683282)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁵, 683282, F₉, 14, 14) (dual of [(683282, 14), 9565863, 15]-NRT-code), using

OA 7-folding and stacking [i] based on linear OA(9⁸⁵, 4782974, F₉, 14) (dual of [4782974, 4782889, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁸⁵, 4782976, F₉, 14) (dual of [4782976, 4782891, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
    1. linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    2. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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 (156, 170, 1366564)-net over F₃	[i]	Trace Code for Nets
2	Digital (78, 92, 683292)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
3	Digital (79, 93, 683298)-net over F₉	[i]
4	Digital (80, 94, 683302)-net over F₉	[i]
5	Digital (81, 95, 683310)-net over F₉	[i]
6	Digital (82, 96, 683312)-net over F₉	[i]