MinT - Information on Result #1226838

Information on Result #1226838

Digital (42, 52, 1810903)-net over F₆₄, using (u,Â u+v)-construction based on

digital (10, 15, 133183)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64¹⁵, 133183, F₆₄, 6, 5) (dual of [(133183, 6), 799083, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(64¹⁵, 133184, F₆₄, 2, 5) (dual of [(133184, 2), 266353, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      3. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      4. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      5. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      6. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      7. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      8. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      9. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      10. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      11. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      12. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      13. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      14. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      15. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      16. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      17. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      18. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      19. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      20. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      21. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      22. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      23. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      24. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      25. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      26. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      27. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      28. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      29. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      30. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      31. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      32. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      33. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      34. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      35. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      36. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      37. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      38. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      39. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      40. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      41. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      42. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      43. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      44. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      45. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      46. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      47. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      48. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      49. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      50. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      51. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      52. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      53. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      54. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      55. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      56. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      57. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      58. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      59. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
      60. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      61. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code) (see above)
      62. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code) (see above)
      63. linear OOA(64³, 2081, F₆₄, 2, 2) (dual of [(2081, 2), 4159, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
        appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
      64. linear OOA(64⁹, 2081, F₆₄, 2, 5) (dual of [(2081, 2), 4153, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
        linear OOA(64⁷, 2016, F₆₄, 2, 5) (dual of [(2016, 2), 4025, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64⁷, 4032, F₆₄, 5) (dual of [4032, 4025, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
digital (27, 37, 1677720)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³⁷, 1677720, F₆₄, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(64³⁷, 8388600, F₆₄, 10) (dual of [8388600, 8388563, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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.