MinT - Information on Result #1194028

Information on Result #1194028

Digital (87, 104, 132864)-net over F₉, using net defined by OOA based on linear OOA(9¹⁰⁴, 132864, F₉, 17, 17) (dual of [(132864, 17), 2258584, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(9¹⁰⁴, 1062913, F₉, 17) (dual of [1062913, 1062809, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹⁰⁴, 1062914, F₉, 17) (dual of [1062914, 1062810, 18]-code), using
  - trace code [i] based on linear OA(81⁵², 531457, F₈₁, 17) (dual of [531457, 531405, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(81⁴⁹, 531442, F₈₁, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(81³⁷, 531442, F₈₁, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(81³, 15, F₈₁, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-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		This result only	Method
1	Digital (88, 105, 132864)-net over F₉	[i]		Net Duplication