MinT - Information on Result #1210443

Information on Result #1210443

Digital (176, 191, 4793554)-net over F₄, using (u,Â u+v)-construction based on

digital (12, 19, 70)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁹, 70, F₄, 9, 7) (dual of [(70, 9), 611, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(4¹⁹, 71, F₄, 3, 7) (dual of [(71, 3), 194, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(4¹, 17, F₄, 3, 1) (dual of [(17, 3), 50, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 3, 1) for arbitrarily large s, using
        appending 2 arbitrary columns [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OOA(4³, 17, F₄, 3, 2) (dual of [(17, 3), 48, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(4³, 21, F₄, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
        appending kth column [i] based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [i]
      3. linear OOA(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
        ovoid in PG(3,Â 4) [i]
      4. linear OOA(4¹¹, 20, F₄, 3, 7) (dual of [(20, 3), 49, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
        linear code embedding found in a computer search [i]
digital (157, 172, 4793484)-net over F₄, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁴³, 1198371, F₂₅₆, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(256⁴³, 8388598, F₂₅₆, 15) (dual of [8388598, 8388555, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.