MinT - Information on Result #1194516

Information on Result #1194516

Digital (79, 104, 1095)-net over F₉, using net defined by OOA based on linear OOA(9¹⁰⁴, 1095, F₉, 25, 25) (dual of [(1095, 25), 27271, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(9¹⁰⁴, 13141, F₉, 25) (dual of [13141, 13037, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹⁰⁴, 13146, F₉, 25) (dual of [13146, 13042, 26]-code), using
  - trace code [i] based on linear OA(81⁵², 6573, F₈₁, 25) (dual of [6573, 6521, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(81⁴⁹, 6562, F₈₁, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(81⁴¹, 6562, F₈₁, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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 (80, 105, 1095)-net over F₉	[i]	Net Duplication
2	Digital (81, 106, 1095)-net over F₉	[i]
3	Digital (82, 107, 1095)-net over F₉	[i]
4	Digital (79, 103, 1095)-net over F₉	[i]	m-Reduction