MinT - Information on Result #1234572

Information on Result #1234572

Digital (48, 58, 4548582)-net over F₁₂₈, using generalized (u,Â u+v)-construction based on

digital (0, 0, 32513)-net over F₁₂₈, using
- s-reduction based on digital (0, 0, s)-net over F₁₂₈ for arbitrarily large s, using
  - arbitrary set of 128⁰ points [i]
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 0, 32513)-net over F₁₂₈ (see above)
digital (0, 1, 32513)-net over F₁₂₈, using
- s-reduction based on digital (0, 1, s)-net over F₁₂₈ for arbitrarily large s, using
  - construction for strength kÂ =Â 1 [i]
digital (0, 1, 32513)-net over F₁₂₈ (see above)
digital (0, 1, 32513)-net over F₁₂₈ (see above)
digital (0, 1, 32513)-net over F₁₂₈ (see above)
digital (0, 1, 32513)-net over F₁₂₈ (see above)
digital (2, 4, 32513)-net over F₁₂₈, using
- s-reduction based on digital (2, 4, 2113665)-net over F₁₂₈, using
  - kÂ =Â 2 construction [i]
digital (2, 4, 32513)-net over F₁₂₈ (see above)
digital (2, 5, 32513)-net over F₁₂₈, using
- s-reduction based on digital (2, 5, 49156)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁵, 49156, F₁₂₈, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁵, 49156, F₁₂₈, 3) (dual of [49156, 49151, 4]-code or 49156-cap in PG(4,128)), using
        large caps in PG(4,Â b) [i]
digital (7, 12, 32513)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128¹², 32513, F₁₂₈, 5, 5) (dual of [(32513, 5), 162553, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(128¹², 32513, F₁₂₈, 4, 5) (dual of [(32513, 4), 130040, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹², 65027, F₁₂₈, 5) (dual of [65027, 65015, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(128¹², 65028, F₁₂₈, 5) (dual of [65028, 65016, 6]-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code) (see above)
        linear OA(128³, 16257, F₁₂₈, 2) (dual of [16257, 16254, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
        linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
digital (18, 28, 419431)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128²⁸, 419431, F₁₂₈, 10, 10) (dual of [(419431, 10), 4194282, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(128²⁸, 2097155, F₁₂₈, 10) (dual of [2097155, 2097127, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
      1. linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(128²⁵, 2097152, F₁₂₈, 9) (dual of [2097152, 2097127, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.