MinT - Information on Result #1229955

Information on Result #1229955

Digital (156, 170, 4797589)-net over F₈, using generalized (u,Â u+v)-construction based on

digital (11, 15, 4105)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁵, 4105, F₈, 4, 4) (dual of [(4105, 4), 16405, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(8¹⁵, 4105, F₈, 3, 4) (dual of [(4105, 3), 12300, 5]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(8³, 73, F₈, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
        appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
        Hamming code H(3,8) [i]
      2. linear OOA(8¹², 4032, F₈, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
        trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
        1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
digital (42, 49, 2396742)-net over F₈, using
- s-reduction based on digital (42, 49, 2796200)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8⁴⁹, 2796200, F₈, 7, 7) (dual of [(2796200, 7), 19573351, 8]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OA(8⁴⁹, 8388601, F₈, 7) (dual of [8388601, 8388552, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁴⁹, large, F₈, 7) (dual of [large, large−49, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
digital (92, 106, 2396742)-net over F₈, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁵³, 1198371, F₆₄, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
    - OA 7-folding and stacking [i] based on linear OA(64⁵³, 8388597, F₆₄, 14) (dual of [8388597, 8388544, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.