Information on Result #1228103

Digital (66, 76, 7591756)-net over F128, using (u, u+v)-construction based on
  1. digital (12, 17, 4194301)-net over F128, using
  2. digital (49, 59, 3795878)-net over F128, using
    • net defined by OOA [i] based on linear OOA(12859, 3795878, F128, 15, 10) (dual of [(3795878, 15), 56938111, 11]-NRT-code), using
      • OOA 2-folding and stacking with additional row [i] based on linear OOA(12859, 7591757, F128, 3, 10) (dual of [(7591757, 3), 22775212, 11]-NRT-code), using
        • discarding factors / shortening the dual code based on linear OOA(12859, 7591758, F128, 3, 10) (dual of [(7591758, 3), 22775215, 11]-NRT-code), using
          • generalized (u, u+v)-construction [i] based on
            1. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code), using
            2. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            3. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            4. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            5. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            6. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            7. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            8. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            9. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            10. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            11. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            12. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            13. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            14. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            15. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            16. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            17. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            18. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            19. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            20. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            21. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            22. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            23. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            24. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            25. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            26. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            27. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            28. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            29. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            30. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            31. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            32. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            33. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            34. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            35. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            36. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            37. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            38. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            39. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            40. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            41. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            42. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            43. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            44. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            45. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            46. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            47. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            48. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            49. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            50. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            51. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            52. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            53. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            54. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            55. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            56. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            57. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            58. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            59. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            60. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            61. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            62. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            63. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            64. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            65. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            66. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            67. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            68. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            69. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            70. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            71. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            72. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            73. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            74. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            75. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            76. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            77. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            78. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            79. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            80. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            81. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            82. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            83. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            84. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            85. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            86. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            87. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            88. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            89. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            90. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            91. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            92. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            93. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            94. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            95. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            96. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            97. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            98. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            99. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            100. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            101. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            102. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            103. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            104. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            105. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            106. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            107. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            108. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            109. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            110. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            111. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            112. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            113. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            114. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            115. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            116. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            117. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            118. linear OOA(1280, 49156, F128, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
            119. linear OOA(1281, 49156, F128, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code), using
            120. linear OOA(1281, 49156, F128, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
            121. linear OOA(1281, 49156, F128, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
            122. linear OOA(1281, 49156, F128, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
            123. linear OOA(1281, 49156, F128, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
            124. linear OOA(1284, 49156, F128, 3, 2) (dual of [(49156, 3), 147464, 3]-NRT-code), using
            125. linear OOA(1284, 49156, F128, 3, 2) (dual of [(49156, 3), 147464, 3]-NRT-code) (see above)
            126. linear OOA(1285, 49156, F128, 3, 3) (dual of [(49156, 3), 147463, 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.