MinT - Information on Result #1228134

Information on Result #1228134

Digital (62, 73, 5469232)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (12, 17, 4194301)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128¹⁷, 4194301, F₁₂₈, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(128¹⁷, 4194301, F₁₂₈, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹⁷, large, F₁₂₈, 5) (dual of [large, large−17, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
digital (45, 56, 2734616)-net over F₁₂₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 15, 1056896)-net over F₁₂₈, using
    - net defined by OOA [i] based on linear OOA(128¹⁵, 1056896, F₁₂₈, 5, 5) (dual of [(1056896, 5), 5284465, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(128¹⁵, 1056896, F₁₂₈, 4, 5) (dual of [(1056896, 4), 4227569, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
        linear OOA(128¹, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] 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 OOA(128¹, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 2]-NRT-code) (see above)
        linear OOA(128¹, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 2]-NRT-code) (see above)
        linear OOA(128³, 8257, F₁₂₈, 4, 2) (dual of [(8257, 4), 33025, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128³, 16513, F₁₂₈, 4, 2) (dual of [(16513, 4), 66049, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(128³, 16513, F₁₂₈, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
        linear OOA(128⁹, 8257, F₁₂₈, 4, 5) (dual of [(8257, 4), 33019, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(128², 129, F₁₂₈, 4, 2) (dual of [(129, 4), 514, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;514,128) [i]
        linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
  2. digital (30, 41, 1677720)-net over F₁₂₈, using
    - net defined by OOA [i] based on linear OOA(128⁴¹, 1677720, F₁₂₈, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(128⁴¹, 8388601, F₁₂₈, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.