MinT - Information on Result #1227619

Information on Result #1227619

Digital (45, 56, 1946802)-net over F₈₁, using (u,Â u+v)-construction based on

digital (10, 15, 269082)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81¹⁵, 269082, F₈₁, 5, 5) (dual of [(269082, 5), 1345395, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(81¹⁵, 269082, F₈₁, 4, 5) (dual of [(269082, 4), 1076313, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 4, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      3. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      4. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      5. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      6. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      7. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      8. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      9. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      10. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      11. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      12. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      13. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      14. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      15. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      16. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      17. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      18. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      19. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      20. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      21. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      22. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      23. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      24. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      25. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      26. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      27. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      28. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      29. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      30. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      31. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      32. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      33. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      34. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      35. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      36. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      37. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      38. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      39. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      40. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      41. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      42. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      43. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      44. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      45. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      46. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      47. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      48. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      49. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      50. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      51. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      52. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      53. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      54. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      55. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      56. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      57. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      58. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      59. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      60. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      61. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      62. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      63. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      64. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      65. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      66. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      67. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      68. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      69. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      70. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      71. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      72. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      73. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      74. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      75. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      76. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
      77. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      78. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code) (see above)
      79. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code) (see above)
      80. linear OOA(81³, 3322, F₈₁, 4, 2) (dual of [(3322, 4), 13285, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 4, 2) (dual of [(6643, 4), 26569, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
      81. linear OOA(81⁹, 3322, F₈₁, 4, 5) (dual of [(3322, 4), 13279, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(81², 82, F₈₁, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;326,81) [i]
        linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
digital (30, 41, 1677720)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁴¹, 1677720, F₈₁, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(81⁴¹, 8388601, F₈₁, 11) (dual of [8388601, 8388560, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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.