MinT - Information on Result #1234626

Information on Result #1234626

Digital (62, 74, 2812712)-net over F₁₂₈, using generalized (u,Â u+v)-construction based on

digital (4, 8, 16512)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁸, 16512, F₁₂₈, 4, 4) (dual of [(16512, 4), 66040, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(128⁸, 16512, F₁₂₈, 3, 4) (dual of [(16512, 3), 49528, 5]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 3, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      3. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      4. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      5. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      6. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      7. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      8. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      9. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      10. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      11. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      12. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      13. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      14. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      15. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      16. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      17. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      18. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      19. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      20. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      21. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      22. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      23. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      24. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      25. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      26. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      27. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      28. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      29. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      30. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      31. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      32. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      33. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      34. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      35. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      36. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      37. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      38. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      39. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      40. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      41. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      42. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      43. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      44. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      45. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      46. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      47. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      48. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      49. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      50. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      51. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      52. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      53. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      54. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      55. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      56. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      57. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      58. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      59. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      60. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      61. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      62. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      63. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      64. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      65. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      66. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      67. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      68. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      69. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      70. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      71. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      72. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      73. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      74. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      75. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      76. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      77. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      78. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      79. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      80. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      81. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      82. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      83. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      84. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      85. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      86. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      87. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      88. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      89. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      90. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      91. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      92. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      93. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      94. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      95. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      96. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      97. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      98. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      99. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      100. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      101. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      102. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      103. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      104. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      105. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      106. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      107. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      108. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      109. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      110. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      111. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      112. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      113. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      114. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      115. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      116. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      117. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      118. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      119. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      120. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      121. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      122. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      123. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      124. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
      125. linear OOA(128¹, 129, F₁₂₈, 3, 1) (dual of [(129, 3), 386, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 3, 1) for arbitrarily large s, using
        appending 2 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]
      126. linear OOA(128¹, 129, F₁₂₈, 3, 1) (dual of [(129, 3), 386, 2]-NRT-code) (see above)
      127. linear OOA(128², 129, F₁₂₈, 3, 2) (dual of [(129, 3), 385, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;385,128) [i]
      128. linear OOA(128⁴, 129, F₁₂₈, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;383,128) [i]
digital (15, 21, 1398100)-net over F₁₂₈, using
- s-reduction based on digital (15, 21, 2796201)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128²¹, 2796201, F₁₂₈, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (33, 45, 1398100)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁴⁵, 1398100, F₁₂₈, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(128⁴⁵, 8388600, F₁₂₈, 12) (dual of [8388600, 8388555, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁴⁵, large, F₁₂₈, 12) (dual of [large, large−45, 13]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.