MinT - Information on Result #1194418

Information on Result #1194418

Digital (73, 96, 1195)-net over F₉, using net defined by OOA based on linear OOA(9⁹⁶, 1195, F₉, 23, 23) (dual of [(1195, 23), 27389, 24]-NRT-code), using

OOA 11-folding and stacking with additional row [i] based on linear OA(9⁹⁶, 13146, F₉, 23) (dual of [13146, 13050, 24]-code), using
- trace code [i] based on linear OA(81⁴⁸, 6573, F₈₁, 23) (dual of [6573, 6525, 24]-code), using
  - constructionÂ X applied to C([0,11]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(81⁴⁵, 6562, F₈₁, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
    2. linear OA(81³⁷, 6562, F₈₁, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(81³, 11, F₈₁, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
      - discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
        Reedâ€“Solomon code RS(78,81) [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 (74, 97, 1195)-net over F₉	[i]	Net Duplication
2	Digital (75, 98, 1195)-net over F₉	[i]
3	Digital (76, 99, 1195)-net over F₉	[i]
4	Digital (73, 95, 1195)-net over F₉	[i]	m-Reduction