MinT - Information on Result #1202830

Information on Result #1202830

Digital (23, 44, 657)-net over F₈₁, using net defined by OOA based on linear OOA(81⁴⁴, 657, F₈₁, 21, 21) (dual of [(657, 21), 13753, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(81⁴⁴, 6571, F₈₁, 21) (dual of [6571, 6527, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁴⁴, 6573, F₈₁, 21) (dual of [6573, 6529, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(81⁴¹, 6562, F₈₁, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(81³, 11, F₈₁, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
      - discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
        Reedâ€“Solomon code RS(78,81) [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 (24, 44, 657)-net over F₈₁	[i]	t-Expansion
2	Digital (24, 45, 657)-net over F₈₁	[i]	Net Duplication
3	Digital (25, 46, 657)-net over F₈₁	[i]	Net Duplication
4	Digital (23, 43, 657)-net over F₈₁	[i]	m-Reduction