MinT - Information on Result #1195740

Information on Result #1195740

Digital (87, 116, 9363)-net over F₁₆, using net defined by OOA based on linear OOA(16¹¹⁶, 9363, F₁₆, 29, 29) (dual of [(9363, 29), 271411, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(16¹¹⁶, 131083, F₁₆, 29) (dual of [131083, 130967, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹⁶, 131084, F₁₆, 29) (dual of [131084, 130968, 30]-code), using
  - trace code [i] based on linear OA(256⁵⁸, 65542, F₂₅₆, 29) (dual of [65542, 65484, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. 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]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (88, 116, 9363)-net over F₁₆	[i]	t-Expansion
2	Digital (88, 117, 9363)-net over F₁₆	[i]	Net Duplication
3	Digital (89, 118, 9363)-net over F₁₆	[i]
4	Digital (90, 119, 9363)-net over F₁₆	[i]
5	Digital (91, 120, 9363)-net over F₁₆	[i]
6	Digital (87, 115, 9363)-net over F₁₆	[i]	m-Reduction