MinT - Information on Result #1203250

Information on Result #1203250

Digital (40, 49, 7242231)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁴⁹, 7242231, F₁₂₈, 12, 9) (dual of [(7242231, 12), 86906723, 10]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(128⁴⁹, 7242232, F₁₂₈, 4, 9) (dual of [(7242232, 4), 28968879, 10]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 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, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  3. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  4. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  5. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  6. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  7. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  8. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  9. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  10. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  11. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  12. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  13. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  14. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  15. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  16. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  17. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  18. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  19. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  20. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  21. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  22. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  23. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  24. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  25. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  26. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  27. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  28. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  29. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  30. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  31. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  32. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  33. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  34. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  35. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  36. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  37. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  38. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  39. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  40. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  41. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  42. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  43. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  44. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  45. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  46. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  47. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  48. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  49. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  50. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  51. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  52. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  53. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  54. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  55. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  56. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  57. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  58. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  59. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  60. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  61. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  62. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  63. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  64. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  65. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  66. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  67. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  68. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  69. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  70. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  71. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  72. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  73. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  74. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  75. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  76. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  77. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  78. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  79. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  80. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  81. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  82. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  83. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  84. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  85. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  86. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  87. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  88. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  89. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  90. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  91. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  92. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  93. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  94. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  95. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  96. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  97. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  98. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  99. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  100. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  101. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  102. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  103. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  104. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  105. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  106. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  107. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  108. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  109. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  110. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  111. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  112. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  113. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  114. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  115. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  116. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  117. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  118. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  119. linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
  120. linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 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]
  121. linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
  122. linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
  123. linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
  124. linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
  125. linear OOA(128⁴, 49156, F₁₂₈, 4, 2) (dual of [(49156, 4), 196620, 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]
  126. linear OOA(128⁵, 49156, F₁₂₈, 4, 3) (dual of [(49156, 4), 196619, 4]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁵, 49156, F₁₂₈, 3) (dual of [49156, 49151, 4]-code or 49156-cap in PG(4,128)), using
        large caps in PG(4,Â b) [i]
  127. linear OOA(128¹⁰, 524288, F₁₂₈, 4, 4) (dual of [(524288, 4), 2097142, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128¹⁰, 1048577, F₁₂₈, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        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(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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]
  128. linear OOA(128²⁵, 524288, F₁₂₈, 4, 9) (dual of [(524288, 4), 2097127, 10]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(128²⁵, 2097152, F₁₂₈, 9) (dual of [2097152, 2097127, 10]-code), using
      - an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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	Digital (53, 62, large)-net over F₁₂₈	[i]		(u,Â u+v)-Construction for Nets