MinT - Information on Result #1180078

Information on Result #1180078

Digital (115, 126, 1677739)-net over F₂, using net defined by OOA based on linear OOA(2¹²⁶, 1677739, F₂, 15, 11) (dual of [(1677739, 15), 25165959, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹²⁶, 1677740, F₂, 5, 11) (dual of [(1677740, 5), 8388574, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 20, F₂, 5, 5) (dual of [(20, 5), 90, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁰, 20, F₂, 4, 5) (dual of [(20, 4), 70, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 10, 20)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹¹⁶, 1677720, F₂, 5, 11) (dual of [(1677720, 5), 8388484, 12]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.