MinT - Information on Result #1195244

Information on Result #1195244

Digital (45, 60, 18726)-net over F₁₆, using net defined by OOA based on linear OOA(16⁶⁰, 18726, F₁₆, 15, 15) (dual of [(18726, 15), 280830, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(16⁶⁰, 131083, F₁₆, 15) (dual of [131083, 131023, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁶⁰, 131084, F₁₆, 15) (dual of [131084, 131024, 16]-code), using
  - trace code [i] based on linear OA(256³⁰, 65542, F₂₅₆, 15) (dual of [65542, 65512, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. 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]
      2. linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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 (46, 61, 18726)-net over F₁₆	[i]	Net Duplication
2	Digital (47, 62, 18726)-net over F₁₆	[i]
3	Digital (48, 63, 18726)-net over F₁₆	[i]