MinT - Information on Result #1202980

Information on Result #1202980

Digital (33, 58, 549)-net over F₈₁, using net defined by OOA based on linear OOA(81⁵⁸, 549, F₈₁, 25, 25) (dual of [(549, 25), 13667, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(81⁵⁸, 6589, F₈₁, 25) (dual of [6589, 6531, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁵⁸, 6591, F₈₁, 25) (dual of [6591, 6533, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,7]) [i] based on
    1. 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]
    2. linear OA(81²⁹, 6562, F₈₁, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(81⁹, 29, F₈₁, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
      - discarding factors / shortening the dual code based on linear OA(81⁹, 81, F₈₁, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
        Reedâ€“Solomon code RS(72,81) [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		Method
1	Digital (34, 58, 549)-net over F₈₁	[i]	t-Expansion
2	Digital (34, 59, 549)-net over F₈₁	[i]	Net Duplication
3	Digital (33, 57, 549)-net over F₈₁	[i]	m-Reduction