MinT - Information on Result #1192976

Information on Result #1192976

Digital (125, 162, 1821)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶², 1821, F₈, 37, 37) (dual of [(1821, 37), 67215, 38]-NRT-code), using

OOA 18-folding and stacking with additional row [i] based on linear OA(8¹⁶², 32779, F₈, 37) (dual of [32779, 32617, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁶², 32780, F₈, 37) (dual of [32780, 32618, 38]-code), using
  - constructionÂ X applied to C([0,18]) âŠ‚ C([0,17]) [i] based on
    1. linear OA(8¹⁶¹, 32769, F₈, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    2. linear OA(8¹⁵¹, 32769, F₈, 35) (dual of [32769, 32618, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
    3. linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 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 (126, 162, 1821)-net over F₈	[i]	t-Expansion
2	Digital (126, 163, 1821)-net over F₈	[i]	Net Duplication
3	Digital (127, 164, 1821)-net over F₈	[i]
4	Digital (128, 165, 1821)-net over F₈	[i]
5	Digital (129, 166, 1821)-net over F₈	[i]
6	Digital (130, 167, 1821)-net over F₈	[i]
7	Digital (125, 161, 1821)-net over F₈	[i]	m-Reduction