MinT - Information on Result #1215165

Information on Result #1215165

Digital (60, 71, 419459)-net over F₈, using (u,Â u+v)-construction based on

digital (2, 7, 28)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁷, 28, F₈, 5, 5) (dual of [(28, 5), 133, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
    - a code by Danev and Olsson [i]
digital (53, 64, 419431)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁶⁴, 419431, F₈, 11, 11) (dual of [(419431, 11), 4613677, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(8⁶⁴, 2097156, F₈, 11) (dual of [2097156, 2097092, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁶⁴, 2097159, F₈, 11) (dual of [2097159, 2097095, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(8⁶⁴, 2097152, F₈, 11) (dual of [2097152, 2097088, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(8⁵⁷, 2097152, F₈, 10) (dual of [2097152, 2097095, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.