MinT - Information on Result #1164434

Information on Result #1164434

Linear OOA(2⁴⁴, 77, F₂, 8, 11) (dual of [(77, 8), 572, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(2⁴⁴, 78, F₂, 5, 11) (dual of [(78, 5), 346, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹², 36, F₂, 5, 5) (dual of [(36, 5), 168, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹², 36, F₂, 4, 5) (dual of [(36, 4), 132, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 12, 36)-net over F₂, using
      - linear code embedding found in a computer search [i]
2. linear OOA(2³², 42, F₂, 5, 11) (dual of [(42, 5), 178, 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(2²², 22, F₂, 5, 11) (dual of [(22, 5), 88, 12]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 22, 22)-net over F₂, using
        a shift-net [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.