MinT - Information on Result #1194304

Information on Result #1194304

Digital (63, 84, 1313)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁴, 1313, F₉, 21, 21) (dual of [(1313, 21), 27489, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(9⁸⁴, 13131, F₉, 21) (dual of [13131, 13047, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁸⁴, 13134, F₉, 21) (dual of [13134, 13050, 22]-code), using
  - trace code [i] based on linear OA(81⁴², 6567, F₈₁, 21) (dual of [6567, 6525, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. 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]
      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(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (64, 85, 1313)-net over F₉	[i]	Net Duplication
2	Digital (65, 86, 1313)-net over F₉	[i]
3	Digital (66, 87, 1313)-net over F₉	[i]
4	Digital (63, 83, 1313)-net over F₉	[i]	m-Reduction