MinT - Information on Result #1199268

Information on Result #1199268

Digital (62, 75, 1398452)-net over F₃₂, using net defined by OOA based on linear OOA(32⁷⁵, 1398452, F₃₂, 14, 13) (dual of [(1398452, 14), 19578253, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(32⁷⁵, 4195357, F₃₂, 2, 13) (dual of [(4195357, 2), 8390639, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32¹⁴, 1056, F₃₂, 2, 6) (dual of [(1056, 2), 2098, 7]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      3. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      4. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      5. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      6. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      7. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      8. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      9. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      10. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      11. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      12. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      13. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      14. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      15. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      16. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      17. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      18. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      19. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      20. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      21. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      22. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      23. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      24. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      25. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      26. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
      27. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      28. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
      29. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
      30. linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
      31. linear OOA(32³, 33, F₃₂, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;63,32) [i]
      32. linear OOA(32⁶, 33, F₃₂, 2, 6) (dual of [(33, 2), 60, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;60,32) [i]
  2. linear OOA(32⁶¹, 4194301, F₃₂, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(32⁶¹, 8388602, F₃₂, 13) (dual of [8388602, 8388541, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁶¹, large, F₃₂, 13) (dual of [large, large−61, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.