MinT - Information on Result #1234826

Information on Result #1234826

Digital (146, 162, 2105470)-net over F₈, using trace code for nets based on digital (65, 81, 1052735)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (12, 20, 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, using
        arbitrary set of 64⁰ points [i]
    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, 1, 65)-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]
    58. digital (0, 1, 65)-net over F₆₄ (see above)
    59. digital (0, 1, 65)-net over F₆₄ (see above)
    60. digital (0, 1, 65)-net over F₆₄ (see above)
    61. digital (0, 2, 65)-net over F₆₄, using
      - kÂ =Â 2 construction [i]
    62. digital (0, 2, 65)-net over F₆₄ (see above)
    63. digital (0, 4, 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]
    64. digital (0, 8, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
2. digital (45, 61, 1048575)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁶¹, 1048575, F₆₄, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
    - OA 8-folding and stacking [i] based on linear OA(64⁶¹, 8388600, F₆₄, 16) (dual of [8388600, 8388539, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁶¹, large, F₆₄, 16) (dual of [large, large−61, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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 (147, 163, 2105470)-net over F₈	[i]		Net Duplication