MinT - Information on Result #1708070

Information on Result #1708070

Digital (10, 15, 2097408)-net over F₁₂₈, using net defined by OOA based on linear OOA(128¹⁵, 2097408, F₁₂₈, 5, 5) (dual of [(2097408, 5), 10487025, 6]-NRT-code), using

appending kth column [i] based on linear OOA(128¹⁵, 2097408, F₁₂₈, 4, 5) (dual of [(2097408, 4), 8389617, 6]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(128¹⁵, 2097408, F₁₂₈, 5) (dual of [2097408, 2097393, 6]-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
    2. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    3. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    4. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    5. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    6. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    7. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    8. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    9. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    10. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    11. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    12. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    13. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    14. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    15. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    16. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    17. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    18. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    19. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    20. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    21. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    22. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    23. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    24. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    25. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    26. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    27. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    28. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    29. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    30. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    31. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    32. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    33. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    34. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    35. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    36. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    37. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    38. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    39. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    40. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    41. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    42. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    43. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    44. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    45. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    46. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    47. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    48. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    49. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    50. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    51. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    52. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    53. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    54. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    55. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    56. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    57. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    58. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    59. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    60. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    61. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    62. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    63. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    64. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    65. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    66. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    67. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    68. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    69. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    70. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    71. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    72. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    73. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    74. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    75. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    76. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    77. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    78. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    79. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    80. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    81. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    82. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    83. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    84. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    85. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    86. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    87. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    88. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    89. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    90. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    91. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    92. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    93. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    94. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    95. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    96. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    97. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    98. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    99. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    100. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    101. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    102. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    103. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    104. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    105. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    106. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    107. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    108. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    109. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    110. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    111. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    112. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    113. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    114. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    115. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    116. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    117. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    118. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    119. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    120. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    121. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    122. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    123. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
    124. linear OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 2]-code), using
      - discarding factors / shortening the dual code 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 OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 2]-code) (see above)
    126. linear OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 2]-code) (see above)
    127. linear OA(128³, 16386, F₁₂₈, 2) (dual of [16386, 16383, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
    128. linear OA(128⁹, 16386, F₁₂₈, 5) (dual of [16386, 16377, 6]-code), using
      - (u,Â u+v)-construction [i] based on
        linear OA(128², 129, F₁₂₈, 2) (dual of [129, 127, 3]-code or 129-arc in PG(1,128)), using
        extended Reedâ€“Solomon code RS_e(127,128) [i]
        Hamming code H(2,128) [i]
        linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]

Mode: 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.