Information on Result #1228105

Digital (67, 77, 8388602)-net over F128, using (u, u+v)-construction based on
  1. digital (12, 17, 4194301)-net over F128, using
  2. digital (50, 60, 4194301)-net over F128, using
    • net defined by OOA [i] based on linear OOA(12860, 4194301, F128, 15, 10) (dual of [(4194301, 15), 62914455, 11]-NRT-code), using
      • OOA 2-folding and stacking with additional row [i] based on linear OOA(12860, large, F128, 3, 10), using
        • generalized (u, u+v)-construction [i] based on
          1. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code), using
          2. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          3. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          4. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          5. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          6. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          7. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          8. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          9. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          10. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          11. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          12. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          13. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          14. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          15. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          16. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          17. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          18. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          19. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          20. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          21. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          22. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          23. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          24. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          25. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          26. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          27. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          28. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          29. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          30. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          31. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          32. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          33. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          34. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          35. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          36. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          37. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          38. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          39. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          40. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          41. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          42. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          43. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          44. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          45. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          46. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          47. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          48. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          49. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          50. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          51. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          52. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          53. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          54. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          55. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          56. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          57. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          58. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          59. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          60. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          61. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          62. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          63. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          64. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          65. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          66. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          67. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          68. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          69. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          70. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          71. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          72. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          73. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          74. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          75. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          76. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          77. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          78. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          79. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          80. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          81. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          82. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          83. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          84. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          85. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          86. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          87. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          88. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          89. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          90. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          91. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          92. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          93. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          94. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          95. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          96. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          97. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          98. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          99. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          100. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          101. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          102. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          103. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          104. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          105. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          106. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          107. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          108. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          109. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          110. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          111. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          112. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          113. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          114. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          115. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          116. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          117. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          118. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
          119. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
          120. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
          121. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
          122. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
          123. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
          124. linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code), using
          125. linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code) (see above)
          126. linear OOA(1286, 699051, F128, 3, 3) (dual of [(699051, 3), 2097147, 4]-NRT-code), using
          127. linear OOA(12813, 699051, F128, 3, 5) (dual of [(699051, 3), 2097140, 6]-NRT-code), using
          128. linear OOA(12828, 699051, F128, 3, 10) (dual of [(699051, 3), 2097125, 11]-NRT-code), using
            • OOA 3-folding [i] based on linear OA(12828, 2097153, F128, 10) (dual of [2097153, 2097125, 11]-code), using
              • discarding factors / shortening the dual code based on linear OA(12828, 2097155, F128, 10) (dual of [2097155, 2097127, 11]-code), using
                • construction X applied to Ce(9) ⊂ Ce(8) [i] based on
                  1. linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
                  2. linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
                  3. linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code) (see above)

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.