MinT - Information on Result #1180116

Information on Result #1180116

Digital (142, 153, 4194345)-net over F₂, using net defined by OOA based on linear OOA(2¹⁵³, 4194345, F₂, 15, 11) (dual of [(4194345, 15), 62915022, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁵³, 4194346, F₂, 5, 11) (dual of [(4194346, 5), 20971577, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
        OOAs constructed from BCH codes [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.