MinT - Information on Result #1194594

Information on Result #1194594

Digital (85, 112, 1011)-net over F₉, using net defined by OOA based on linear OOA(9¹¹², 1011, F₉, 27, 27) (dual of [(1011, 27), 27185, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(9¹¹², 13144, F₉, 27) (dual of [13144, 13032, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹², 13146, F₉, 27) (dual of [13146, 13034, 28]-code), using
  - trace code [i] based on linear OA(81⁵⁶, 6573, F₈₁, 27) (dual of [6573, 6517, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
      1. linear OA(81⁵³, 6562, F₈₁, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. 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]
      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 (86, 113, 1011)-net over F₉	[i]	Net Duplication
2	Digital (87, 114, 1011)-net over F₉	[i]
3	Digital (88, 115, 1011)-net over F₉	[i]
4	Digital (85, 111, 1011)-net over F₉	[i]	m-Reduction