MinT - Information on Result #1159618

Information on Result #1159618

Linear OOA(2⁵⁹, 100, F₂, 7, 13) (dual of [(100, 7), 641, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁸, 64, F₂, 7, 6) (dual of [(64, 7), 430, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(2¹⁸, 64, F₂, 6, 6) (dual of [(64, 6), 366, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹⁸, 64, F₂, 5, 6) (dual of [(64, 5), 302, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 18, 64)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2⁴¹, 50, F₂, 7, 13) (dual of [(50, 7), 309, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 21, F₂, 7, 6) (dual of [(21, 7), 135, 7]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(2¹², 21, F₂, 6, 6) (dual of [(21, 6), 114, 7]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹², 21, F₂, 5, 6) (dual of [(21, 5), 93, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 12, 21)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁹, 29, F₂, 7, 13) (dual of [(29, 7), 174, 14]-NRT-code), using
    - extracting embedded OOA [i] based on digital (16, 29, 29)-net over F₂, using
      - a shift-net [i]

Mode: Constructive and linear.

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