MinT - Information on Result #1159470

Information on Result #1159470

Linear OOA(2⁴⁵, 84, F₂, 7, 11) (dual of [(84, 7), 543, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹³, 45, F₂, 7, 5) (dual of [(45, 7), 302, 6]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2¹³, 45, F₂, 5, 5) (dual of [(45, 5), 212, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹³, 45, F₂, 4, 5) (dual of [(45, 4), 167, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 13, 45)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2³², 42, F₂, 7, 11) (dual of [(42, 7), 262, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 20, F₂, 7, 5) (dual of [(20, 7), 130, 6]-NRT-code), using
    - appending 2 arbitrary columns [i] based on 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, 7, 11) (dual of [(22, 7), 132, 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.

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