MinT - Information on Result #1109772

Information on Result #1109772

Linear OOA(2³⁷, 41, F₂, 5, 12) (dual of [(41, 5), 168, 13]-NRT-code), using extracting embedded OOA based on digital (25, 37, 41)-net over F₂, using

s-reduction based on digital (25, 37, 45)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2³⁷, 45, F₂, 18, 12) (dual of [(45, 18), 773, 13]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2³⁷, 46, F₂, 6, 12) (dual of [(46, 6), 239, 13]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. 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(2²⁵, 25, F₂, 6, 12) (dual of [(25, 6), 125, 13]-NRT-code), using
        extracting embedded OOA [i] based on digital (13, 25, 25)-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.