MinT - Information on Result #1200866

Information on Result #1200866

Digital (15, 20, 8388602)-net over F₆₄, using net defined by OOA based on linear OOA(64²⁰, 8388602, F₆₄, 6, 5) (dual of [(8388602, 6), 50331592, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(64²⁰, large, F₆₄, 2, 5), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 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, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  58. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  59. linear OOA(64⁰, 131073, F₆₄, 2, 0) (dual of [(131073, 2), 262146, 1]-NRT-code) (see above)
  60. linear OOA(64¹, 131073, F₆₄, 2, 1) (dual of [(131073, 2), 262145, 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, 131073, F₆₄, 2, 1) (dual of [(131073, 2), 262145, 2]-NRT-code) (see above)
  62. linear OOA(64¹, 131073, F₆₄, 2, 1) (dual of [(131073, 2), 262145, 2]-NRT-code) (see above)
  63. linear OOA(64⁴, 131073, F₆₄, 2, 2) (dual of [(131073, 2), 262142, 3]-NRT-code), using
    - discarding factors / shortening the dual code 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]
  64. linear OOA(64¹³, 131073, F₆₄, 2, 5) (dual of [(131073, 2), 262133, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(64¹³, 262146, F₆₄, 5) (dual of [262146, 262133, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹³, 262147, F₆₄, 5) (dual of [262147, 262134, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(64¹³, 262144, F₆₄, 5) (dual of [262144, 262131, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(64¹⁰, 262144, F₆₄, 4) (dual of [262144, 262134, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (17, 22, large)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets