MinT - Information on Result #1194148

Information on Result #1194148

Digital (57, 76, 1459)-net over F₉, using net defined by OOA based on linear OOA(9⁷⁶, 1459, F₉, 19, 19) (dual of [(1459, 19), 27645, 20]-NRT-code), using

OOA 9-folding and stacking with additional row [i] based on linear OA(9⁷⁶, 13132, F₉, 19) (dual of [13132, 13056, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁷⁶, 13134, F₉, 19) (dual of [13134, 13058, 20]-code), using
  - trace code [i] based on linear OA(81³⁸, 6567, F₈₁, 19) (dual of [6567, 6529, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
      1. 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]
      2. linear OA(81³³, 6562, F₈₁, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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 (58, 77, 1459)-net over F₉	[i]	Net Duplication
2	Digital (59, 78, 1459)-net over F₉	[i]
3	Digital (60, 79, 1459)-net over F₉	[i]
4	Digital (57, 75, 1459)-net over F₉	[i]	m-Reduction