MinT - Information on Result #1228094

Information on Result #1228094

Digital (42, 52, 2734616)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (10, 15, 1056896)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128¹⁵, 1056896, F₁₂₈, 5, 5) (dual of [(1056896, 5), 5284465, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(128¹⁵, 1056896, F₁₂₈, 4, 5) (dual of [(1056896, 4), 4227569, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 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, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      3. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      4. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      5. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      6. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      7. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      8. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      9. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      10. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      11. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      12. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      13. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      14. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      15. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      16. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      17. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      18. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      19. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      20. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      21. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      22. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      23. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      24. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      25. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      26. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      27. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      28. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      29. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      30. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      31. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      32. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      33. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      34. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      35. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      36. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      37. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      38. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      39. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      40. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      41. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      42. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      43. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      44. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      45. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      46. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      47. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      48. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      49. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      50. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      51. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      52. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      53. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      54. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      55. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      56. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      57. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      58. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      59. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      60. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      61. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      62. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      63. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      64. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      65. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      66. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      67. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      68. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      69. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      70. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      71. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      72. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      73. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      74. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      75. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      76. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      77. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      78. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      79. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      80. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      81. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      82. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      83. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      84. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      85. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      86. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      87. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      88. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      89. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      90. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      91. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      92. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      93. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      94. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      95. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      96. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      97. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      98. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      99. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      100. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      101. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      102. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      103. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      104. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      105. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      106. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      107. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      108. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      109. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      110. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      111. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      112. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      113. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      114. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      115. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      116. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      117. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      118. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      119. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      120. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      121. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      122. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      123. linear OOA(128⁰, 8257, F₁₂₈, 4, 0) (dual of [(8257, 4), 33028, 1]-NRT-code) (see above)
      124. linear OOA(128¹, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 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, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 2]-NRT-code) (see above)
      126. linear OOA(128¹, 8257, F₁₂₈, 4, 1) (dual of [(8257, 4), 33027, 2]-NRT-code) (see above)
      127. linear OOA(128³, 8257, F₁₂₈, 4, 2) (dual of [(8257, 4), 33025, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128³, 16513, F₁₂₈, 4, 2) (dual of [(16513, 4), 66049, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(128³, 16513, F₁₂₈, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
      128. linear OOA(128⁹, 8257, F₁₂₈, 4, 5) (dual of [(8257, 4), 33019, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(128², 129, F₁₂₈, 4, 2) (dual of [(129, 4), 514, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;514,128) [i]
        linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
digital (27, 37, 1677720)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128³⁷, 1677720, F₁₂₈, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(128³⁷, 8388600, F₁₂₈, 10) (dual of [8388600, 8388563, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(128³⁷, large, F₁₂₈, 10) (dual of [large, large−37, 11]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (59, 69, 5469232)-net over F₁₂₈	[i]		(u,Â u+v)-Construction for Nets