MinT - Information on Result #1206311

Information on Result #1206311

Digital (217, 236, 932112)-net over F₂, using (u,Â u+v)-construction based on

digital (19, 28, 46)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²⁸, 46, F₂, 9, 9) (dual of [(46, 9), 386, 10]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²⁸, 46, F₂, 8, 9) (dual of [(46, 8), 340, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 23, F₂, 8, 4) (dual of [(23, 8), 175, 5]-NRT-code), using
        appending 4 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, 23, F₂, 8, 9) (dual of [(23, 8), 165, 10]-NRT-code), using
        extracting embedded OOA [i] based on digital (10, 19, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
digital (189, 208, 932066)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²⁰⁸, 932066, F₂, 19, 19) (dual of [(932066, 19), 17709046, 20]-NRT-code), using
  - OOA 9-folding and stacking with additional row [i] based on linear OA(2²⁰⁸, 8388595, F₂, 19) (dual of [8388595, 8388387, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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.