MinT - Information on Result #1197068

Information on Result #1197068

Digital (57, 86, 1117)-net over F₂₅, using net defined by OOA based on linear OOA(25⁸⁶, 1117, F₂₅, 29, 29) (dual of [(1117, 29), 32307, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(25⁸⁶, 15639, F₂₅, 29) (dual of [15639, 15553, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁸⁶, 15641, F₂₅, 29) (dual of [15641, 15555, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(23) [i] based on
    1. 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]
    2. linear OA(25⁷⁰, 15625, F₂₅, 24) (dual of [15625, 15555, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    3. linear OA(25⁴, 16, F₂₅, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
      - discarding factors / shortening the dual code based on linear OA(25⁴, 25, F₂₅, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
        Reedâ€“Solomon code RS(21,25) [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 (58, 86, 1117)-net over F₂₅	[i]	t-Expansion
2	Digital (58, 87, 1117)-net over F₂₅	[i]	Net Duplication
3	Digital (59, 88, 1117)-net over F₂₅	[i]
4	Digital (60, 89, 1117)-net over F₂₅	[i]
5	Digital (57, 85, 1117)-net over F₂₅	[i]	m-Reduction
6	Digital (75, 104, 1183)-net over F₂₅	[i]	(u,Â u+v)-Construction for Nets