MinT - Information on Result #1200954

Information on Result #1200954

Digital (27, 34, 5592575)-net over F₆₄, using net defined by OOA based on linear OOA(64³⁴, 5592575, F₆₄, 9, 7) (dual of [(5592575, 9), 50333141, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(64³⁴, 5592576, F₆₄, 3, 7) (dual of [(5592576, 3), 16777694, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 87384, F₆₄, 3, 0) (dual of [(87384, 3), 262152, 1]-NRT-code) (see above)
  58. linear OOA(64¹, 87384, F₆₄, 3, 1) (dual of [(87384, 3), 262151, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [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]
  59. linear OOA(64¹, 87384, F₆₄, 3, 1) (dual of [(87384, 3), 262151, 2]-NRT-code) (see above)
  60. linear OOA(64¹, 87384, F₆₄, 3, 1) (dual of [(87384, 3), 262151, 2]-NRT-code) (see above)
  61. linear OOA(64¹, 87384, F₆₄, 3, 1) (dual of [(87384, 3), 262151, 2]-NRT-code) (see above)
  62. linear OOA(64⁴, 87384, F₆₄, 3, 2) (dual of [(87384, 3), 262148, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 266305, F₆₄, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(64⁴, 266305, F₆₄, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
        appending kth column [i] based on linear OA(64⁴, 266305, F₆₄, 2) (dual of [266305, 266301, 3]-code), using
        Hamming code H(4,64) [i]
  63. linear OOA(64⁶, 87384, F₆₄, 3, 3) (dual of [(87384, 3), 262146, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 270401, F₆₄, 3, 3) (dual of [(270401, 3), 811197, 4]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OA(64⁶, 270402, F₆₄, 3) (dual of [270402, 270396, 4]-code or 270402-cap in PG(5,64)), using
        large caps in PG(5,Â b) [i]
  64. linear OOA(64²⁰, 87384, F₆₄, 3, 7) (dual of [(87384, 3), 262132, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64²⁰, 262152, F₆₄, 7) (dual of [262152, 262132, 8]-code), using
      - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
        linear OA(64¹⁹, 262145, F₆₄, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
        linear OA(64¹³, 262145, F₆₄, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)

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.