MinT - Information on Result #1226834

Information on Result #1226834

Digital (38, 48, 1683769)-net over F₆₄, using (u,Â u+v)-construction based on

digital (6, 11, 6049)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64¹¹, 6049, F₆₄, 5, 5) (dual of [(6049, 5), 30234, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(64¹¹, 12099, F₆₄, 5) (dual of [12099, 12088, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(64³, 4033, F₆₄, 2) (dual of [4033, 4030, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
      3. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
digital (27, 37, 1677720)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³⁷, 1677720, F₆₄, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(64³⁷, 8388600, F₆₄, 10) (dual of [8388600, 8388563, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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.