MinT - Information on Result #1204860

Information on Result #1204860

Digital (25, 46, 6555)-net over F₂₅₆, using net defined by OOA based on linear OOA(256⁴⁶, 6555, F₂₅₆, 21, 21) (dual of [(6555, 21), 137609, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(256⁴⁶, 65551, F₂₅₆, 21) (dual of [65551, 65505, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(256⁴⁶, 65554, F₂₅₆, 21) (dual of [65554, 65508, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
    1. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(256⁵, 17, F₂₅₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
      - discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
        Reedâ€“Solomon code RS(251,256) [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 (26, 46, 6555)-net over F₂₅₆	[i]	t-Expansion
2	Digital (26, 47, 6555)-net over F₂₅₆	[i]	Net Duplication
3	Digital (27, 48, 6555)-net over F₂₅₆	[i]	Net Duplication
4	Digital (25, 45, 6555)-net over F₂₅₆	[i]	m-Reduction