MinT - Information on Result #1234447

Information on Result #1234447

Digital (56, 70, 1202546)-net over F₆₄, using (u,Â u+v)-construction based on

digital (10, 17, 4175)-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, 0, 65)-net over F₆₄ (see above)
  58. 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]
  59. digital (0, 1, 65)-net over F₆₄ (see above)
  60. digital (0, 1, 65)-net over F₆₄ (see above)
  61. digital (0, 1, 65)-net over F₆₄ (see above)
  62. digital (0, 2, 65)-net over F₆₄, using
    - kÂ =Â 2 construction [i]
  63. digital (0, 3, 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 (1, 8, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
digital (39, 53, 1198371)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁵³, 1198371, F₆₄, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(64⁵³, 8388597, F₆₄, 14) (dual of [8388597, 8388544, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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	(70, 84, 1202546)-net in base 32	[i]		Base Change