MinT - Information on Result #1200858

Information on Result #1200858

Digital (10, 15, 133183)-net over F₆₄, using net defined by OOA 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
      1. 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]
      2. 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]

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 (42, 52, 1810903)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets
2	Digital (45, 56, 1810903)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets