MinT - Information on Result #1217503

Information on Result #1217503

Digital (116, 130, 2397479)-net over F₉, using (u,Â u+v)-construction based on

digital (17, 24, 737)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9²⁴, 737, F₉, 9, 7) (dual of [(737, 9), 6609, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(9²⁴, 738, F₉, 3, 7) (dual of [(738, 3), 2190, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁰, 82, F₉, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁰, s, F₉, 3, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(9⁰, 82, F₉, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
      3. linear OOA(9¹, 82, F₉, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 3, 1) for arbitrarily large s, using
        appending 2 arbitrary columns [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]
      4. linear OOA(9¹, 82, F₉, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
      5. linear OOA(9¹, 82, F₉, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
      6. linear OOA(9¹, 82, F₉, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
      7. linear OOA(9³, 82, F₉, 3, 2) (dual of [(82, 3), 243, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9³, 91, F₉, 3, 2) (dual of [(91, 3), 270, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(9³, 91, F₉, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
        appending kth column [i] based on linear OA(9³, 91, F₉, 2) (dual of [91, 88, 3]-code), using
        Hamming code H(3,9) [i]
      8. linear OOA(9⁴, 82, F₉, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
        ovoid in PG(3,Â 9) [i]
      9. linear OOA(9¹³, 82, F₉, 3, 7) (dual of [(82, 3), 233, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 13, 82)-net over F₉, using
        base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) for nets [i] based on digital (0, 7, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
digital (92, 106, 2396742)-net over F₉, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81⁵³, 1198371, F₈₁, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
    - OA 7-folding and stacking [i] based on linear OA(81⁵³, 8388597, F₈₁, 14) (dual of [8388597, 8388544, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁵³, large, F₈₁, 14) (dual of [large, large−53, 15]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.