MinT - Information on Result #1214425

Information on Result #1214425

Digital (54, 63, 1441223)-net over F₇, using (u,Â u+v)-construction based on

digital (2, 6, 21)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁶, 21, F₇, 4, 4) (dual of [(21, 4), 78, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(7⁶, 21, F₇, 3, 4) (dual of [(21, 3), 57, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(7⁶, 42, F₇, 4) (dual of [42, 36, 5]-code), using
      - 1 times truncation [i] based on linear OA(7⁷, 43, F₇, 5) (dual of [43, 36, 6]-code), using
        a code by Danev and Olsson [i]
digital (48, 57, 1441202)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁵⁷, 1441202, F₇, 9, 9) (dual of [(1441202, 9), 12970761, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(7⁵⁷, 5764809, F₇, 9) (dual of [5764809, 5764752, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(7⁵⁷, 5764801, F₇, 9) (dual of [5764801, 5764744, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(7⁴⁹, 5764801, F₇, 8) (dual of [5764801, 5764752, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(7⁰, 8, F₇, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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.