MinT - Information on Result #1234671

Information on Result #1234671

Digital (55, 69, 1214883)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (9, 16, 16512)-net over F₁₂₈, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 129)-net over F₁₂₈, using
    - s-reduction based on digital (0, 0, s)-net over F₁₂₈ for arbitrarily large s, using
      - arbitrary set of 128⁰ points [i]
  2. digital (0, 0, 129)-net over F₁₂₈ (see above)
  3. digital (0, 0, 129)-net over F₁₂₈ (see above)
  4. digital (0, 0, 129)-net over F₁₂₈ (see above)
  5. digital (0, 0, 129)-net over F₁₂₈ (see above)
  6. digital (0, 0, 129)-net over F₁₂₈ (see above)
  7. digital (0, 0, 129)-net over F₁₂₈ (see above)
  8. digital (0, 0, 129)-net over F₁₂₈ (see above)
  9. digital (0, 0, 129)-net over F₁₂₈ (see above)
  10. digital (0, 0, 129)-net over F₁₂₈ (see above)
  11. digital (0, 0, 129)-net over F₁₂₈ (see above)
  12. digital (0, 0, 129)-net over F₁₂₈ (see above)
  13. digital (0, 0, 129)-net over F₁₂₈ (see above)
  14. digital (0, 0, 129)-net over F₁₂₈ (see above)
  15. digital (0, 0, 129)-net over F₁₂₈ (see above)
  16. digital (0, 0, 129)-net over F₁₂₈ (see above)
  17. digital (0, 0, 129)-net over F₁₂₈ (see above)
  18. digital (0, 0, 129)-net over F₁₂₈ (see above)
  19. digital (0, 0, 129)-net over F₁₂₈ (see above)
  20. digital (0, 0, 129)-net over F₁₂₈ (see above)
  21. digital (0, 0, 129)-net over F₁₂₈ (see above)
  22. digital (0, 0, 129)-net over F₁₂₈ (see above)
  23. digital (0, 0, 129)-net over F₁₂₈ (see above)
  24. digital (0, 0, 129)-net over F₁₂₈ (see above)
  25. digital (0, 0, 129)-net over F₁₂₈ (see above)
  26. digital (0, 0, 129)-net over F₁₂₈ (see above)
  27. digital (0, 0, 129)-net over F₁₂₈ (see above)
  28. digital (0, 0, 129)-net over F₁₂₈ (see above)
  29. digital (0, 0, 129)-net over F₁₂₈ (see above)
  30. digital (0, 0, 129)-net over F₁₂₈ (see above)
  31. digital (0, 0, 129)-net over F₁₂₈ (see above)
  32. digital (0, 0, 129)-net over F₁₂₈ (see above)
  33. digital (0, 0, 129)-net over F₁₂₈ (see above)
  34. digital (0, 0, 129)-net over F₁₂₈ (see above)
  35. digital (0, 0, 129)-net over F₁₂₈ (see above)
  36. digital (0, 0, 129)-net over F₁₂₈ (see above)
  37. digital (0, 0, 129)-net over F₁₂₈ (see above)
  38. digital (0, 0, 129)-net over F₁₂₈ (see above)
  39. digital (0, 0, 129)-net over F₁₂₈ (see above)
  40. digital (0, 0, 129)-net over F₁₂₈ (see above)
  41. digital (0, 0, 129)-net over F₁₂₈ (see above)
  42. digital (0, 0, 129)-net over F₁₂₈ (see above)
  43. digital (0, 0, 129)-net over F₁₂₈ (see above)
  44. digital (0, 0, 129)-net over F₁₂₈ (see above)
  45. digital (0, 0, 129)-net over F₁₂₈ (see above)
  46. digital (0, 0, 129)-net over F₁₂₈ (see above)
  47. digital (0, 0, 129)-net over F₁₂₈ (see above)
  48. digital (0, 0, 129)-net over F₁₂₈ (see above)
  49. digital (0, 0, 129)-net over F₁₂₈ (see above)
  50. digital (0, 0, 129)-net over F₁₂₈ (see above)
  51. digital (0, 0, 129)-net over F₁₂₈ (see above)
  52. digital (0, 0, 129)-net over F₁₂₈ (see above)
  53. digital (0, 0, 129)-net over F₁₂₈ (see above)
  54. digital (0, 0, 129)-net over F₁₂₈ (see above)
  55. digital (0, 0, 129)-net over F₁₂₈ (see above)
  56. digital (0, 0, 129)-net over F₁₂₈ (see above)
  57. digital (0, 0, 129)-net over F₁₂₈ (see above)
  58. digital (0, 0, 129)-net over F₁₂₈ (see above)
  59. digital (0, 0, 129)-net over F₁₂₈ (see above)
  60. digital (0, 0, 129)-net over F₁₂₈ (see above)
  61. digital (0, 0, 129)-net over F₁₂₈ (see above)
  62. digital (0, 0, 129)-net over F₁₂₈ (see above)
  63. digital (0, 0, 129)-net over F₁₂₈ (see above)
  64. digital (0, 0, 129)-net over F₁₂₈ (see above)
  65. digital (0, 0, 129)-net over F₁₂₈ (see above)
  66. digital (0, 0, 129)-net over F₁₂₈ (see above)
  67. digital (0, 0, 129)-net over F₁₂₈ (see above)
  68. digital (0, 0, 129)-net over F₁₂₈ (see above)
  69. digital (0, 0, 129)-net over F₁₂₈ (see above)
  70. digital (0, 0, 129)-net over F₁₂₈ (see above)
  71. digital (0, 0, 129)-net over F₁₂₈ (see above)
  72. digital (0, 0, 129)-net over F₁₂₈ (see above)
  73. digital (0, 0, 129)-net over F₁₂₈ (see above)
  74. digital (0, 0, 129)-net over F₁₂₈ (see above)
  75. digital (0, 0, 129)-net over F₁₂₈ (see above)
  76. digital (0, 0, 129)-net over F₁₂₈ (see above)
  77. digital (0, 0, 129)-net over F₁₂₈ (see above)
  78. digital (0, 0, 129)-net over F₁₂₈ (see above)
  79. digital (0, 0, 129)-net over F₁₂₈ (see above)
  80. digital (0, 0, 129)-net over F₁₂₈ (see above)
  81. digital (0, 0, 129)-net over F₁₂₈ (see above)
  82. digital (0, 0, 129)-net over F₁₂₈ (see above)
  83. digital (0, 0, 129)-net over F₁₂₈ (see above)
  84. digital (0, 0, 129)-net over F₁₂₈ (see above)
  85. digital (0, 0, 129)-net over F₁₂₈ (see above)
  86. digital (0, 0, 129)-net over F₁₂₈ (see above)
  87. digital (0, 0, 129)-net over F₁₂₈ (see above)
  88. digital (0, 0, 129)-net over F₁₂₈ (see above)
  89. digital (0, 0, 129)-net over F₁₂₈ (see above)
  90. digital (0, 0, 129)-net over F₁₂₈ (see above)
  91. digital (0, 0, 129)-net over F₁₂₈ (see above)
  92. digital (0, 0, 129)-net over F₁₂₈ (see above)
  93. digital (0, 0, 129)-net over F₁₂₈ (see above)
  94. digital (0, 0, 129)-net over F₁₂₈ (see above)
  95. digital (0, 0, 129)-net over F₁₂₈ (see above)
  96. digital (0, 0, 129)-net over F₁₂₈ (see above)
  97. digital (0, 0, 129)-net over F₁₂₈ (see above)
  98. digital (0, 0, 129)-net over F₁₂₈ (see above)
  99. digital (0, 0, 129)-net over F₁₂₈ (see above)
  100. digital (0, 0, 129)-net over F₁₂₈ (see above)
  101. digital (0, 0, 129)-net over F₁₂₈ (see above)
  102. digital (0, 0, 129)-net over F₁₂₈ (see above)
  103. digital (0, 0, 129)-net over F₁₂₈ (see above)
  104. digital (0, 0, 129)-net over F₁₂₈ (see above)
  105. digital (0, 0, 129)-net over F₁₂₈ (see above)
  106. digital (0, 0, 129)-net over F₁₂₈ (see above)
  107. digital (0, 0, 129)-net over F₁₂₈ (see above)
  108. digital (0, 0, 129)-net over F₁₂₈ (see above)
  109. digital (0, 0, 129)-net over F₁₂₈ (see above)
  110. digital (0, 0, 129)-net over F₁₂₈ (see above)
  111. digital (0, 0, 129)-net over F₁₂₈ (see above)
  112. digital (0, 0, 129)-net over F₁₂₈ (see above)
  113. digital (0, 0, 129)-net over F₁₂₈ (see above)
  114. digital (0, 0, 129)-net over F₁₂₈ (see above)
  115. digital (0, 0, 129)-net over F₁₂₈ (see above)
  116. digital (0, 0, 129)-net over F₁₂₈ (see above)
  117. digital (0, 0, 129)-net over F₁₂₈ (see above)
  118. digital (0, 0, 129)-net over F₁₂₈ (see above)
  119. digital (0, 0, 129)-net over F₁₂₈ (see above)
  120. digital (0, 0, 129)-net over F₁₂₈ (see above)
  121. digital (0, 0, 129)-net over F₁₂₈ (see above)
  122. digital (0, 1, 129)-net over F₁₂₈, using
    - s-reduction based on digital (0, 1, s)-net over F₁₂₈ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  123. digital (0, 1, 129)-net over F₁₂₈ (see above)
  124. digital (0, 1, 129)-net over F₁₂₈ (see above)
  125. digital (0, 1, 129)-net over F₁₂₈ (see above)
  126. digital (0, 2, 129)-net over F₁₂₈, using
    - kÂ =Â 2 construction [i]
  127. digital (0, 3, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
      - Niederreiter sequence [i]
  128. digital (0, 7, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
digital (39, 53, 1198371)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁵³, 1198371, F₁₂₈, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(128⁵³, 8388597, F₁₂₈, 14) (dual of [8388597, 8388544, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁵³, large, F₁₂₈, 14) (dual of [large, large−53, 15]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’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

None.