MinT - Information on Result #1218772

Information on Result #1218772

Digital (68, 78, 4399935)-net over F₁₆, using (u,Â u+v)-construction based on

digital (17, 22, 1044495)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16²², 1044495, F₁₆, 6, 5) (dual of [(1044495, 6), 6266948, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(16²², 1044496, F₁₆, 2, 5) (dual of [(1044496, 2), 2088970, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(16⁰, s, F₁₆, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      3. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      4. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      5. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      6. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      7. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      8. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      9. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      10. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      11. linear OOA(16⁰, 65281, F₁₆, 2, 0) (dual of [(65281, 2), 130562, 1]-NRT-code) (see above)
      12. linear OOA(16¹, 65281, F₁₆, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(16¹, s, F₁₆, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      13. linear OOA(16¹, 65281, F₁₆, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code) (see above)
      14. linear OOA(16¹, 65281, F₁₆, 2, 1) (dual of [(65281, 2), 130561, 2]-NRT-code) (see above)
      15. linear OOA(16⁵, 65281, F₁₆, 2, 2) (dual of [(65281, 2), 130557, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(16⁵, 69905, F₁₆, 2, 2) (dual of [(69905, 2), 139805, 3]-NRT-code), using
        appending kth column [i] based on linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
        Hamming code H(5,16) [i]
      16. linear OOA(16¹⁴, 65281, F₁₆, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
        trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
digital (46, 56, 3355440)-net over F₁₆, using
- trace code for nets [i] based on digital (18, 28, 1677720)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256²⁸, 1677720, F₂₅₆, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(256²⁸, 8388600, F₂₅₆, 10) (dual of [8388600, 8388572, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(256²⁸, large, F₂₅₆, 10) (dual of [large, large−28, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.