MinT - Information on Result #1215201

Information on Result #1215201

Digital (111, 122, 6710936)-net over F₈, using (u,Â u+v)-construction based on

digital (28, 33, 4194301)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8³³, 4194301, F₈, 5, 5) (dual of [(4194301, 5), 20971472, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8³³, large, F₈, 5) (dual of [large, large−33, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (78, 89, 3355468)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. digital (71, 82, 3355440)-net over F₈, using
    - trace code for nets [i] based on digital (30, 41, 1677720)-net over F₆₄, using
      - net defined by OOA [i] based on linear OOA(64⁴¹, 1677720, F₆₄, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
        OOA 5-folding and stacking with additional row [i] based on linear OA(64⁴¹, 8388601, F₆₄, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.