MinT - Information on Result #1213665

Information on Result #1213665

Digital (123, 138, 1198470)-net over F₅, using (u,Â u+v)-construction based on

digital (11, 18, 99)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹⁸, 99, F₅, 9, 7) (dual of [(99, 9), 873, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(5¹⁸, 100, F₅, 3, 7) (dual of [(100, 3), 282, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
        appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OOA(5³, 25, F₅, 3, 2) (dual of [(25, 3), 72, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(5³, 31, F₅, 3, 2) (dual of [(31, 3), 90, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
      3. linear OOA(5⁴, 25, F₅, 3, 3) (dual of [(25, 3), 71, 4]-NRT-code), using
        OOA stacking with additional row [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
      4. linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
        linear code embedding found in a computer search [i]
digital (105, 120, 1198371)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹²⁰, 1198371, F₅, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(5¹²⁰, 8388598, F₅, 15) (dual of [8388598, 8388478, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹²⁰, large, F₅, 15) (dual of [large, large−120, 16]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,15], 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.