MinT - Information on Result #1181410

Information on Result #1181410

Digital (180, 197, 1048583)-net over F₂, using net defined by OOA based on linear OOA(2¹⁹⁷, 1048583, F₂, 24, 17) (dual of [(1048583, 24), 25165795, 18]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁹⁷, 1048584, F₂, 8, 17) (dual of [(1048584, 8), 8388475, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 9, F₂, 8, 8) (dual of [(9, 8), 60, 9]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹², 9, F₂, 7, 8) (dual of [(9, 7), 51, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 12, 9)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸⁵, 1048575, F₂, 8, 17) (dual of [(1048575, 8), 8388415, 18]-NRT-code), using
    - OOA 8-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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

None.