Information on Result #1228073

Digital (53, 62, large)-net over F128, using (u, u+v)-construction based on
  1. digital (9, 13, 4194301)-net over F128, using
  2. digital (40, 49, 7242231)-net over F128, using
    • net defined by OOA [i] 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, u+v)-construction [i] based on
          1. linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code), using
          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
          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
          126. linear OOA(1285, 49156, F128, 4, 3) (dual of [(49156, 4), 196619, 4]-NRT-code), using
          127. linear OOA(12810, 524288, F128, 4, 4) (dual of [(524288, 4), 2097142, 5]-NRT-code), using
          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 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]

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:

ResultThis
result
only
Method
1Digital (54, 62, large)-net over F128 [i]t-Expansion
2Digital (55, 62, large)-net over F128 [i]
3Digital (56, 62, large)-net over F128 [i]
4Digital (57, 62, large)-net over F128 [i]
5Digital (58, 62, large)-net over F128 [i]
6Digital (59, 62, large)-net over F128 [i]
7Digital (53, 61, large)-net over F128 [i]m-Reduction
8Digital (53, 60, large)-net over F128 [i]
9Digital (53, 59, large)-net over F128 [i]
10Digital (53, 58, large)-net over F128 [i]
11Digital (53, 57, large)-net over F128 [i]
12Digital (53, 56, large)-net over F128 [i]