MinT - Information on Result #1217350

Information on Result #1217350

Digital (95, 106, 3413858)-net over F₉, using (u,Â u+v)-construction based on

digital (19, 24, 58418)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9²⁴, 58418, F₉, 6, 5) (dual of [(58418, 6), 350484, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(9²⁴, 58419, F₉, 2, 5) (dual of [(58419, 2), 116814, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁰, s, F₉, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
      3. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
      4. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
      5. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      6. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
      7. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
      8. linear OOA(9⁵, 6491, F₉, 2, 2) (dual of [(6491, 2), 12977, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁵, 7381, F₉, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
        appending kth column [i] based on linear OA(9⁵, 7381, F₉, 2) (dual of [7381, 7376, 3]-code), using
        Hamming code H(5,9) [i]
      9. linear OOA(9¹⁶, 6491, F₉, 2, 5) (dual of [(6491, 2), 12966, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(9², 10, F₉, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;18,9) [i]
        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 (71, 82, 3355440)-net over F₉, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81⁴¹, 1677720, F₈₁, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(81⁴¹, 8388601, F₈₁, 11) (dual of [8388601, 8388560, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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.