MinT - Information on Result #1202978

Information on Result #1202978

Digital (29, 54, 548)-net over F₈₁, using net defined by OOA based on linear OOA(81⁵⁴, 548, F₈₁, 25, 25) (dual of [(548, 25), 13646, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(81⁵⁴, 6577, F₈₁, 25) (dual of [6577, 6523, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁵⁴, 6579, F₈₁, 25) (dual of [6579, 6525, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [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(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(81⁵, 17, F₈₁, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
      - discarding factors / shortening the dual code based on linear OA(81⁵, 81, F₈₁, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
        Reedâ€“Solomon code RS(76,81) [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 (30, 54, 548)-net over F₈₁	[i]	t-Expansion
2	Digital (30, 55, 548)-net over F₈₁	[i]	Net Duplication
3	Digital (31, 56, 548)-net over F₈₁	[i]
4	Digital (32, 57, 548)-net over F₈₁	[i]
5	Digital (29, 53, 548)-net over F₈₁	[i]	m-Reduction