MinT - Information on Result #3267583

Information on Result #3267583

Digital (38, 49, 1685848)-net over F₁₂₈, using 128¹ times duplication based on digital (37, 48, 1685848)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (2, 7, 8128)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁷, 8128, F₁₂₈, 5, 5) (dual of [(8128, 5), 40633, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
2. digital (30, 41, 1677720)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁴¹, 1677720, F₁₂₈, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(128⁴¹, 8388601, F₁₂₈, 11) (dual of [8388601, 8388560, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’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.