MinT - Information on Result #1185574

Information on Result #1185574

Digital (174, 205, 3938)-net over F₃, using net defined by OOA based on linear OOA(3²⁰⁵, 3938, F₃, 31, 31) (dual of [(3938, 31), 121873, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(3²⁰⁵, 59071, F₃, 31) (dual of [59071, 58866, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3²⁰⁵, 59073, F₃, 31) (dual of [59073, 58868, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [i] based on
    1. linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(3⁴, 24, F₃, 2) (dual of [24, 20, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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 (175, 205, 3938)-net over F₃	[i]	t-Expansion
2	Digital (175, 206, 3938)-net over F₃	[i]	Net Duplication
3	Digital (176, 207, 3938)-net over F₃	[i]
4	Digital (177, 208, 3938)-net over F₃	[i]
5	Digital (174, 204, 3938)-net over F₃	[i]	m-Reduction