MinT - Information on Result #1214514

Information on Result #1214514

Digital (68, 79, 1152974)-net over F₇, using (u,Â u+v)-construction based on

digital (1, 6, 13)-net over F₇, using
- 7 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
  - a shift-net [i]
digital (62, 73, 1152961)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁷³, 1152961, F₇, 11, 11) (dual of [(1152961, 11), 12682498, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(7⁷³, 5764806, F₇, 11) (dual of [5764806, 5764733, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁷³, 5764809, F₇, 11) (dual of [5764809, 5764736, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(7⁷³, 5764801, F₇, 11) (dual of [5764801, 5764728, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(7⁶⁵, 5764801, F₇, 10) (dual of [5764801, 5764736, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        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.