MinT - Information on Result #1194592

Information on Result #1194592

Digital (81, 108, 1010)-net over F₉, using net defined by OOA based on linear OOA(9¹⁰⁸, 1010, F₉, 27, 27) (dual of [(1010, 27), 27162, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(9¹⁰⁸, 13131, F₉, 27) (dual of [13131, 13023, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹⁰⁸, 13134, F₉, 27) (dual of [13134, 13026, 28]-code), using
  - trace code [i] based on linear OA(81⁵⁴, 6567, F₈₁, 27) (dual of [6567, 6513, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [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(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]
      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 (82, 109, 1010)-net over F₉	[i]	Net Duplication
2	Digital (83, 110, 1010)-net over F₉	[i]
3	Digital (84, 111, 1010)-net over F₉	[i]
4	Digital (81, 107, 1010)-net over F₉	[i]	m-Reduction