MinT - Information on Result #1194596

Information on Result #1194596

Digital (89, 116, 1012)-net over F₉, using net defined by OOA based on linear OOA(9¹¹⁶, 1012, F₉, 27, 27) (dual of [(1012, 27), 27208, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(9¹¹⁶, 13157, F₉, 27) (dual of [13157, 13041, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹¹⁶, 13158, F₉, 27) (dual of [13158, 13042, 28]-code), using
  - trace code [i] based on linear OA(81⁵⁸, 6579, F₈₁, 27) (dual of [6579, 6521, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,10]) [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(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(81⁵, 17, F₈₁, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
        discarding factors / shortening the dual code based on linear OA(81⁵, 81, F₈₁, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
        Reedâ€“Solomon code RS(76,81) [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 (90, 117, 1012)-net over F₉	[i]		Net Duplication
2	Digital (91, 118, 1012)-net over F₉	[i]		Net Duplication