MinT - Information on Result #1179724

Information on Result #1179724

Digital (15, 20, large)-net over F₁₂₈, using net defined by OOA based on linear OOA(128²⁰, large, F₁₂₈, 5, 5), using

appending kth column [i] based on linear OOA(128²⁰, large, F₁₂₈, 4, 5), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  3. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  4. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  5. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  6. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  7. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  8. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  9. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  10. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  11. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  12. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  13. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  14. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  15. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  16. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  17. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  18. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  19. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  20. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  21. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  22. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  23. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  24. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  25. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  26. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  27. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  28. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  29. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  30. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  31. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  32. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  33. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  34. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  35. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  36. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  37. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  38. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  39. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  40. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  41. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  42. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  43. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  44. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  45. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  46. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  47. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  48. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  49. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  50. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  51. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  52. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  53. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  54. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  55. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  56. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  57. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  58. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  59. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  60. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  61. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  62. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  63. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  64. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  65. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  66. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  67. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  68. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  69. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  70. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  71. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  72. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  73. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  74. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  75. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  76. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  77. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  78. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  79. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  80. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  81. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  82. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  83. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  84. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  85. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  86. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  87. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  88. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  89. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  90. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  91. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  92. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  93. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  94. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  95. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  96. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  97. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  98. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  99. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  100. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  101. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  102. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  103. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  104. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  105. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  106. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  107. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  108. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  109. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  110. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  111. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  112. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  113. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  114. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  115. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  116. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  117. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  118. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  119. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  120. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  121. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  122. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  123. linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
  124. linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s, using
      - appending 3 arbitrary columns [i] based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  125. linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code) (see above)
  126. linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code) (see above)
  127. linear OOA(128⁴, 1048577, F₁₂₈, 4, 2) (dual of [(1048577, 4), 4194304, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(128⁴, 2113665, F₁₂₈, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128⁴, 2113665, F₁₂₈, 2) (dual of [2113665, 2113661, 3]-code), using
        Hamming code H(4,128) [i]
  128. linear OOA(128¹³, 1048577, F₁₂₈, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
      - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (16, 20, large)-net over F₁₂₈	[i]	t-Expansion
2	Digital (17, 20, large)-net over F₁₂₈	[i]	t-Expansion
3	Digital (16, 21, large)-net over F₁₂₈	[i]	Net Duplication
4	Digital (17, 22, large)-net over F₁₂₈	[i]
5	Digital (18, 23, large)-net over F₁₂₈	[i]
6	Digital (19, 24, large)-net over F₁₂₈	[i]
7	Digital (20, 25, large)-net over F₁₂₈	[i]
8	Digital (21, 26, large)-net over F₁₂₈	[i]
9	Digital (22, 27, large)-net over F₁₂₈	[i]
10	Digital (15, 19, large)-net over F₁₂₈	[i]	m-Reduction
11	Digital (15, 18, large)-net over F₁₂₈	[i]	m-Reduction