MinT - Information on Result #1206159

Information on Result #1206159

Digital (196, 212, 1048628)-net over F₂, using (u,Â u+v)-construction based on

digital (20, 28, 53)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²⁸, 53, F₂, 8, 8) (dual of [(53, 8), 396, 9]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²⁸, 53, F₂, 7, 8) (dual of [(53, 7), 343, 9]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 23, F₂, 7, 4) (dual of [(23, 7), 152, 5]-NRT-code), using
        appending 3 arbitrary columns [i] based on linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2¹⁹, 30, F₂, 7, 8) (dual of [(30, 7), 191, 9]-NRT-code), using
        extracting embedded OOA [i] based on digital (11, 19, 30)-net over F₂, using
        linear code embedding found in a computer search [i]
digital (168, 184, 1048575)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2¹⁸⁴, 1048575, F₂, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
  - OA 8-folding and stacking [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.