MinT - Information on Result #3261717

Information on Result #3261717

Digital (154, 171, 2105470)-net over F₈, using 8¹ times duplication based on digital (153, 170, 2105470)-net over F₈, using

trace code for nets [i] based on digital (68, 85, 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 (48, 65, 1048575)-net over F₆₄, using
    - net defined by OOA [i] based on linear OOA(64⁶⁵, 1048575, F₆₄, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
      - OOA 8-folding and stacking with additional row [i] based on linear OA(64⁶⁵, 8388601, F₆₄, 17) (dual of [8388601, 8388536, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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.