MinT - Information on Result #1215188

Information on Result #1215188

Digital (93, 104, 3387703)-net over F₈, using (u,Â u+v)-construction based on

digital (17, 22, 32263)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8²², 32263, F₈, 6, 5) (dual of [(32263, 6), 193556, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(8²², 32264, F₈, 2, 5) (dual of [(32264, 2), 64506, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(8⁰, 4033, F₈, 2, 0) (dual of [(4033, 2), 8066, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁰, s, F₈, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(8⁰, 4033, F₈, 2, 0) (dual of [(4033, 2), 8066, 1]-NRT-code) (see above)
      3. linear OOA(8⁰, 4033, F₈, 2, 0) (dual of [(4033, 2), 8066, 1]-NRT-code) (see above)
      4. linear OOA(8¹, 4033, F₈, 2, 1) (dual of [(4033, 2), 8065, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      5. linear OOA(8¹, 4033, F₈, 2, 1) (dual of [(4033, 2), 8065, 2]-NRT-code) (see above)
      6. linear OOA(8¹, 4033, F₈, 2, 1) (dual of [(4033, 2), 8065, 2]-NRT-code) (see above)
      7. linear OOA(8⁵, 4033, F₈, 2, 2) (dual of [(4033, 2), 8061, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁵, 4681, F₈, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
        appending kth column [i] based on linear OA(8⁵, 4681, F₈, 2) (dual of [4681, 4676, 3]-code), using
        Hamming code H(5,8) [i]
      8. linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
        trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
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.