MinT - Information on Result #1197114

Information on Result #1197114

Digital (58, 89, 1042)-net over F₂₅, using net defined by OOA based on linear OOA(25⁸⁹, 1042, F₂₅, 31, 31) (dual of [(1042, 31), 32213, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(25⁸⁹, 15631, F₂₅, 31) (dual of [15631, 15542, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁸⁹, 15632, F₂₅, 31) (dual of [15632, 15543, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
    1. linear OA(25⁸⁸, 15625, F₂₅, 31) (dual of [15625, 15537, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(25⁸², 15625, F₂₅, 29) (dual of [15625, 15543, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(25¹, 7, F₂₅, 1) (dual of [7, 6, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (59, 89, 1042)-net over F₂₅	[i]	t-Expansion
2	Digital (59, 90, 1042)-net over F₂₅	[i]	Net Duplication
3	Digital (60, 91, 1042)-net over F₂₅	[i]
4	Digital (61, 92, 1042)-net over F₂₅	[i]
5	Digital (62, 93, 1042)-net over F₂₅	[i]
6	Digital (58, 88, 1042)-net over F₂₅	[i]	m-Reduction
7	Digital (77, 108, 1108)-net over F₂₅	[i]	(u,Â u+v)-Construction for Nets