MinT - Information on Result #1184644

Information on Result #1184644

Digital (94, 113, 2189)-net over F₃, using net defined by OOA based on linear OOA(3¹¹³, 2189, F₃, 19, 19) (dual of [(2189, 19), 41478, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(3¹¹³, 19702, F₃, 19) (dual of [19702, 19589, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹¹³, 19705, F₃, 19) (dual of [19705, 19592, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹⁰⁹, 19683, F₃, 19) (dual of [19683, 19574, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 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 (95, 113, 2189)-net over F₃	[i]	t-Expansion
2	Digital (95, 114, 2189)-net over F₃	[i]	Net Duplication
3	Digital (96, 115, 2189)-net over F₃	[i]
4	Digital (97, 116, 2189)-net over F₃	[i]
5	Digital (94, 112, 2189)-net over F₃	[i]	m-Reduction