MinT - Information on Result #1000312

Information on Result #1000312

Linear OOA(2⁴⁴, 49, F₂, 3, 13) (dual of [(49, 3), 103, 14]-NRT-code), using extracting embedded OOA based on digital (31, 44, 49)-net over F₂, using

s-reduction based on digital (31, 44, 57)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2⁴⁴, 57, F₂, 18, 13) (dual of [(57, 18), 982, 14]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁴⁴, 58, F₂, 6, 13) (dual of [(58, 6), 304, 14]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2¹⁵, 36, F₂, 6, 6) (dual of [(36, 6), 201, 7]-NRT-code), using
        appending kth column [i] based on linear OOA(2¹⁵, 36, F₂, 5, 6) (dual of [(36, 5), 165, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (9, 15, 36)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2²⁹, 29, F₂, 6, 13) (dual of [(29, 6), 145, 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.

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.