MinT - Information on Result #1217293

Information on Result #1217293

Digital (82, 92, 3362740)-net over F₉, using (u,Â u+v)-construction based on

digital (13, 18, 7300)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹⁸, 7300, F₉, 6, 5) (dual of [(7300, 6), 43782, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(9¹⁸, 7301, F₉, 2, 5) (dual of [(7301, 2), 14584, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁴, 820, F₉, 2, 2) (dual of [(820, 2), 1636, 3]-NRT-code), using
        appending kth column [i] based on linear OA(9⁴, 820, F₉, 2) (dual of [820, 816, 3]-code), using
        Hamming code H(4,9) [i]
      2. linear OOA(9¹⁴, 6481, F₉, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
digital (64, 74, 3355440)-net over F₉, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81³⁷, 1677720, F₈₁, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(81³⁷, 8388600, F₈₁, 10) (dual of [8388600, 8388563, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.