MinT - Information on Result #1195702

Information on Result #1195702

Digital (85, 112, 10084)-net over F₁₆, using net defined by OOA based on linear OOA(16¹¹², 10084, F₁₆, 27, 27) (dual of [(10084, 27), 272156, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(16¹¹², 131093, F₁₆, 27) (dual of [131093, 130981, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹², 131096, F₁₆, 27) (dual of [131096, 130984, 28]-code), using
  - trace code [i] based on linear OA(256⁵⁶, 65548, F₂₅₆, 27) (dual of [65548, 65492, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,11]) [i] based on
      1. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [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 (86, 113, 10084)-net over F₁₆	[i]	Net Duplication
2	Digital (87, 114, 10084)-net over F₁₆	[i]
3	Digital (88, 115, 10084)-net over F₁₆	[i]
4	Digital (85, 111, 10084)-net over F₁₆	[i]	m-Reduction