MinT - Information on Result #1234552

Information on Result #1234552

Digital (58, 73, 1205013)-net over F₈₁, using (u,Â u+v)-construction based on

digital (9, 16, 6642)-net over F₈₁, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 82)-net over F₈₁, using
    - s-reduction based on digital (0, 0, s)-net over F₈₁ for arbitrarily large s, using
      - arbitrary set of 81⁰ points [i]
  2. digital (0, 0, 82)-net over F₈₁ (see above)
  3. digital (0, 0, 82)-net over F₈₁ (see above)
  4. digital (0, 0, 82)-net over F₈₁ (see above)
  5. digital (0, 0, 82)-net over F₈₁ (see above)
  6. digital (0, 0, 82)-net over F₈₁ (see above)
  7. digital (0, 0, 82)-net over F₈₁ (see above)
  8. digital (0, 0, 82)-net over F₈₁ (see above)
  9. digital (0, 0, 82)-net over F₈₁ (see above)
  10. digital (0, 0, 82)-net over F₈₁ (see above)
  11. digital (0, 0, 82)-net over F₈₁ (see above)
  12. digital (0, 0, 82)-net over F₈₁ (see above)
  13. digital (0, 0, 82)-net over F₈₁ (see above)
  14. digital (0, 0, 82)-net over F₈₁ (see above)
  15. digital (0, 0, 82)-net over F₈₁ (see above)
  16. digital (0, 0, 82)-net over F₈₁ (see above)
  17. digital (0, 0, 82)-net over F₈₁ (see above)
  18. digital (0, 0, 82)-net over F₈₁ (see above)
  19. digital (0, 0, 82)-net over F₈₁ (see above)
  20. digital (0, 0, 82)-net over F₈₁ (see above)
  21. digital (0, 0, 82)-net over F₈₁ (see above)
  22. digital (0, 0, 82)-net over F₈₁ (see above)
  23. digital (0, 0, 82)-net over F₈₁ (see above)
  24. digital (0, 0, 82)-net over F₈₁ (see above)
  25. digital (0, 0, 82)-net over F₈₁ (see above)
  26. digital (0, 0, 82)-net over F₈₁ (see above)
  27. digital (0, 0, 82)-net over F₈₁ (see above)
  28. digital (0, 0, 82)-net over F₈₁ (see above)
  29. digital (0, 0, 82)-net over F₈₁ (see above)
  30. digital (0, 0, 82)-net over F₈₁ (see above)
  31. digital (0, 0, 82)-net over F₈₁ (see above)
  32. digital (0, 0, 82)-net over F₈₁ (see above)
  33. digital (0, 0, 82)-net over F₈₁ (see above)
  34. digital (0, 0, 82)-net over F₈₁ (see above)
  35. digital (0, 0, 82)-net over F₈₁ (see above)
  36. digital (0, 0, 82)-net over F₈₁ (see above)
  37. digital (0, 0, 82)-net over F₈₁ (see above)
  38. digital (0, 0, 82)-net over F₈₁ (see above)
  39. digital (0, 0, 82)-net over F₈₁ (see above)
  40. digital (0, 0, 82)-net over F₈₁ (see above)
  41. digital (0, 0, 82)-net over F₈₁ (see above)
  42. digital (0, 0, 82)-net over F₈₁ (see above)
  43. digital (0, 0, 82)-net over F₈₁ (see above)
  44. digital (0, 0, 82)-net over F₈₁ (see above)
  45. digital (0, 0, 82)-net over F₈₁ (see above)
  46. digital (0, 0, 82)-net over F₈₁ (see above)
  47. digital (0, 0, 82)-net over F₈₁ (see above)
  48. digital (0, 0, 82)-net over F₈₁ (see above)
  49. digital (0, 0, 82)-net over F₈₁ (see above)
  50. digital (0, 0, 82)-net over F₈₁ (see above)
  51. digital (0, 0, 82)-net over F₈₁ (see above)
  52. digital (0, 0, 82)-net over F₈₁ (see above)
  53. digital (0, 0, 82)-net over F₈₁ (see above)
  54. digital (0, 0, 82)-net over F₈₁ (see above)
  55. digital (0, 0, 82)-net over F₈₁ (see above)
  56. digital (0, 0, 82)-net over F₈₁ (see above)
  57. digital (0, 0, 82)-net over F₈₁ (see above)
  58. digital (0, 0, 82)-net over F₈₁ (see above)
  59. digital (0, 0, 82)-net over F₈₁ (see above)
  60. digital (0, 0, 82)-net over F₈₁ (see above)
  61. digital (0, 0, 82)-net over F₈₁ (see above)
  62. digital (0, 0, 82)-net over F₈₁ (see above)
  63. digital (0, 0, 82)-net over F₈₁ (see above)
  64. digital (0, 0, 82)-net over F₈₁ (see above)
  65. digital (0, 0, 82)-net over F₈₁ (see above)
  66. digital (0, 0, 82)-net over F₈₁ (see above)
  67. digital (0, 0, 82)-net over F₈₁ (see above)
  68. digital (0, 0, 82)-net over F₈₁ (see above)
  69. digital (0, 0, 82)-net over F₈₁ (see above)
  70. digital (0, 0, 82)-net over F₈₁ (see above)
  71. digital (0, 0, 82)-net over F₈₁ (see above)
  72. digital (0, 0, 82)-net over F₈₁ (see above)
  73. digital (0, 0, 82)-net over F₈₁ (see above)
  74. digital (0, 0, 82)-net over F₈₁ (see above)
  75. digital (0, 1, 82)-net over F₈₁, using
    - s-reduction based on digital (0, 1, s)-net over F₈₁ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  76. digital (0, 1, 82)-net over F₈₁ (see above)
  77. digital (0, 1, 82)-net over F₈₁ (see above)
  78. digital (0, 1, 82)-net over F₈₁ (see above)
  79. digital (0, 2, 82)-net over F₈₁, using
    - kÂ =Â 2 construction [i]
  80. digital (0, 3, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
  81. digital (0, 7, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
digital (42, 57, 1198371)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁵⁷, 1198371, F₈₁, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(81⁵⁷, 8388598, F₈₁, 15) (dual of [8388598, 8388541, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.