MinT - Information on Result #1234458

Information on Result #1234458

Digital (43, 53, 1943960)-net over F₆₄, using (u,Â u+v)-construction based on

digital (11, 16, 266240)-net over F₆₄, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 4160)-net over F₆₄, using
    - s-reduction based on digital (0, 0, s)-net over F₆₄ for arbitrarily large s, using
      - arbitrary set of 64⁰ points [i]
  2. digital (0, 0, 4160)-net over F₆₄ (see above)
  3. digital (0, 0, 4160)-net over F₆₄ (see above)
  4. digital (0, 0, 4160)-net over F₆₄ (see above)
  5. digital (0, 0, 4160)-net over F₆₄ (see above)
  6. digital (0, 0, 4160)-net over F₆₄ (see above)
  7. digital (0, 0, 4160)-net over F₆₄ (see above)
  8. digital (0, 0, 4160)-net over F₆₄ (see above)
  9. digital (0, 0, 4160)-net over F₆₄ (see above)
  10. digital (0, 0, 4160)-net over F₆₄ (see above)
  11. digital (0, 0, 4160)-net over F₆₄ (see above)
  12. digital (0, 0, 4160)-net over F₆₄ (see above)
  13. digital (0, 0, 4160)-net over F₆₄ (see above)
  14. digital (0, 0, 4160)-net over F₆₄ (see above)
  15. digital (0, 0, 4160)-net over F₆₄ (see above)
  16. digital (0, 0, 4160)-net over F₆₄ (see above)
  17. digital (0, 0, 4160)-net over F₆₄ (see above)
  18. digital (0, 0, 4160)-net over F₆₄ (see above)
  19. digital (0, 0, 4160)-net over F₆₄ (see above)
  20. digital (0, 0, 4160)-net over F₆₄ (see above)
  21. digital (0, 0, 4160)-net over F₆₄ (see above)
  22. digital (0, 0, 4160)-net over F₆₄ (see above)
  23. digital (0, 0, 4160)-net over F₆₄ (see above)
  24. digital (0, 0, 4160)-net over F₆₄ (see above)
  25. digital (0, 0, 4160)-net over F₆₄ (see above)
  26. digital (0, 0, 4160)-net over F₆₄ (see above)
  27. digital (0, 0, 4160)-net over F₆₄ (see above)
  28. digital (0, 0, 4160)-net over F₆₄ (see above)
  29. digital (0, 0, 4160)-net over F₆₄ (see above)
  30. digital (0, 0, 4160)-net over F₆₄ (see above)
  31. digital (0, 0, 4160)-net over F₆₄ (see above)
  32. digital (0, 0, 4160)-net over F₆₄ (see above)
  33. digital (0, 0, 4160)-net over F₆₄ (see above)
  34. digital (0, 0, 4160)-net over F₆₄ (see above)
  35. digital (0, 0, 4160)-net over F₆₄ (see above)
  36. digital (0, 0, 4160)-net over F₆₄ (see above)
  37. digital (0, 0, 4160)-net over F₆₄ (see above)
  38. digital (0, 0, 4160)-net over F₆₄ (see above)
  39. digital (0, 0, 4160)-net over F₆₄ (see above)
  40. digital (0, 0, 4160)-net over F₆₄ (see above)
  41. digital (0, 0, 4160)-net over F₆₄ (see above)
  42. digital (0, 0, 4160)-net over F₆₄ (see above)
  43. digital (0, 0, 4160)-net over F₆₄ (see above)
  44. digital (0, 0, 4160)-net over F₆₄ (see above)
  45. digital (0, 0, 4160)-net over F₆₄ (see above)
  46. digital (0, 0, 4160)-net over F₆₄ (see above)
  47. digital (0, 0, 4160)-net over F₆₄ (see above)
  48. digital (0, 0, 4160)-net over F₆₄ (see above)
  49. digital (0, 0, 4160)-net over F₆₄ (see above)
  50. digital (0, 0, 4160)-net over F₆₄ (see above)
  51. digital (0, 0, 4160)-net over F₆₄ (see above)
  52. digital (0, 0, 4160)-net over F₆₄ (see above)
  53. digital (0, 0, 4160)-net over F₆₄ (see above)
  54. digital (0, 0, 4160)-net over F₆₄ (see above)
  55. digital (0, 0, 4160)-net over F₆₄ (see above)
  56. digital (0, 0, 4160)-net over F₆₄ (see above)
  57. digital (0, 0, 4160)-net over F₆₄ (see above)
  58. digital (0, 0, 4160)-net over F₆₄ (see above)
  59. digital (0, 0, 4160)-net over F₆₄ (see above)
  60. digital (0, 1, 4160)-net over F₆₄, using
    - s-reduction based on digital (0, 1, s)-net over F₆₄ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  61. digital (0, 1, 4160)-net over F₆₄ (see above)
  62. digital (0, 1, 4160)-net over F₆₄ (see above)
  63. digital (1, 3, 4160)-net over F₆₄, using
    - s-reduction based on digital (1, 3, 4161)-net over F₆₄, using
      - kÂ =Â 2 construction [i]
  64. digital (5, 10, 4160)-net over F₆₄, using
    - generalized (u,Â u+v)-construction [i] based on
      1. digital (0, 0, 65)-net over F₆₄, using
        s-reduction based on digital (0, 0, s)-net over F₆₄ for arbitrarily large s (see above)
      2. digital (0, 0, 65)-net over F₆₄ (see above)
      3. digital (0, 0, 65)-net over F₆₄ (see above)
      4. digital (0, 0, 65)-net over F₆₄ (see above)
      5. digital (0, 0, 65)-net over F₆₄ (see above)
      6. digital (0, 0, 65)-net over F₆₄ (see above)
      7. digital (0, 0, 65)-net over F₆₄ (see above)
      8. digital (0, 0, 65)-net over F₆₄ (see above)
      9. digital (0, 0, 65)-net over F₆₄ (see above)
      10. digital (0, 0, 65)-net over F₆₄ (see above)
      11. digital (0, 0, 65)-net over F₆₄ (see above)
      12. digital (0, 0, 65)-net over F₆₄ (see above)
      13. digital (0, 0, 65)-net over F₆₄ (see above)
      14. digital (0, 0, 65)-net over F₆₄ (see above)
      15. digital (0, 0, 65)-net over F₆₄ (see above)
      16. digital (0, 0, 65)-net over F₆₄ (see above)
      17. digital (0, 0, 65)-net over F₆₄ (see above)
      18. digital (0, 0, 65)-net over F₆₄ (see above)
      19. digital (0, 0, 65)-net over F₆₄ (see above)
      20. digital (0, 0, 65)-net over F₆₄ (see above)
      21. digital (0, 0, 65)-net over F₆₄ (see above)
      22. digital (0, 0, 65)-net over F₆₄ (see above)
      23. digital (0, 0, 65)-net over F₆₄ (see above)
      24. digital (0, 0, 65)-net over F₆₄ (see above)
      25. digital (0, 0, 65)-net over F₆₄ (see above)
      26. digital (0, 0, 65)-net over F₆₄ (see above)
      27. digital (0, 0, 65)-net over F₆₄ (see above)
      28. digital (0, 0, 65)-net over F₆₄ (see above)
      29. digital (0, 0, 65)-net over F₆₄ (see above)
      30. digital (0, 0, 65)-net over F₆₄ (see above)
      31. digital (0, 0, 65)-net over F₆₄ (see above)
      32. digital (0, 0, 65)-net over F₆₄ (see above)
      33. digital (0, 0, 65)-net over F₆₄ (see above)
      34. digital (0, 0, 65)-net over F₆₄ (see above)
      35. digital (0, 0, 65)-net over F₆₄ (see above)
      36. digital (0, 0, 65)-net over F₆₄ (see above)
      37. digital (0, 0, 65)-net over F₆₄ (see above)
      38. digital (0, 0, 65)-net over F₆₄ (see above)
      39. digital (0, 0, 65)-net over F₆₄ (see above)
      40. digital (0, 0, 65)-net over F₆₄ (see above)
      41. digital (0, 0, 65)-net over F₆₄ (see above)
      42. digital (0, 0, 65)-net over F₆₄ (see above)
      43. digital (0, 0, 65)-net over F₆₄ (see above)
      44. digital (0, 0, 65)-net over F₆₄ (see above)
      45. digital (0, 0, 65)-net over F₆₄ (see above)
      46. digital (0, 0, 65)-net over F₆₄ (see above)
      47. digital (0, 0, 65)-net over F₆₄ (see above)
      48. digital (0, 0, 65)-net over F₆₄ (see above)
      49. digital (0, 0, 65)-net over F₆₄ (see above)
      50. digital (0, 0, 65)-net over F₆₄ (see above)
      51. digital (0, 0, 65)-net over F₆₄ (see above)
      52. digital (0, 0, 65)-net over F₆₄ (see above)
      53. digital (0, 0, 65)-net over F₆₄ (see above)
      54. digital (0, 0, 65)-net over F₆₄ (see above)
      55. digital (0, 0, 65)-net over F₆₄ (see above)
      56. digital (0, 0, 65)-net over F₆₄ (see above)
      57. digital (0, 0, 65)-net over F₆₄ (see above)
      58. digital (0, 0, 65)-net over F₆₄ (see above)
      59. digital (0, 0, 65)-net over F₆₄ (see above)
      60. digital (0, 1, 65)-net over F₆₄, using
        s-reduction based on digital (0, 1, s)-net over F₆₄ for arbitrarily large s (see above)
      61. digital (0, 1, 65)-net over F₆₄ (see above)
      62. digital (0, 1, 65)-net over F₆₄ (see above)
      63. digital (0, 2, 65)-net over F₆₄, using
        kÂ =Â 2 construction [i]
      64. digital (0, 5, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [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.