MinT - Best Known (34, 34+9, s)-Nets in Base 128

Best Known (34, 34+9, s)-Nets in Base 128

(34, 34+9, 3145727)-Net over F₁₂₈ — Constructive and digital

Digital (34, 43, 3145727)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (6, 10, 1048577)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128¹⁰, 1048577, F₁₂₈, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. digital (24, 33, 2097150)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128³³, 2097150, F₁₂₈, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
    - OOA 4-folding and stacking with additional row [i] based on linear OA(128³³, 8388601, F₁₂₈, 9) (dual of [8388601, 8388568, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(128³³, large, F₁₂₈, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

(34, 34+9, 4194815)-Net in Base 128 — Constructive

(34, 43, 4194815)-net in base 128, using

net defined by OOA [i] based on OOA(128⁴³, 4194815, S₁₂₈, 12, 9), using
- OOA stacking with additional row [i] based on OOA(128⁴³, 4194816, S₁₂₈, 4, 9), using
  - discarding parts of the base [i] based on linear OOA(256³⁷, 4194816, F₂₅₆, 4, 9) (dual of [(4194816, 4), 16779227, 10]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 4, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      3. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      4. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      5. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      6. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      7. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      8. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      9. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      10. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      11. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      12. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      13. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      14. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      15. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      16. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      17. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      18. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      19. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      20. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      21. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      22. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      23. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      24. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      25. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      26. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      27. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      28. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      29. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      30. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      31. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      32. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      33. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      34. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      35. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      36. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      37. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      38. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      39. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      40. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      41. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      42. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      43. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      44. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      45. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      46. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      47. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      48. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      49. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      50. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      51. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      52. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      53. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      54. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      55. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      56. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      57. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      58. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      59. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      60. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      61. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      62. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      63. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      64. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      65. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      66. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      67. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      68. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      69. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      70. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      71. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      72. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      73. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      74. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      75. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      76. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      77. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      78. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      79. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      80. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      81. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      82. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      83. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      84. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      85. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      86. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      87. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      88. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      89. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      90. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      91. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      92. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      93. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      94. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      95. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      96. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      97. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      98. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      99. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      100. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      101. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      102. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      103. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      104. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      105. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      106. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      107. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      108. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      109. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      110. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      111. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      112. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      113. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      114. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      115. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      116. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      117. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      118. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      119. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      120. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      121. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      122. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      123. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      124. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      125. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      126. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      127. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      128. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      129. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      130. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      131. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      132. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      133. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      134. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      135. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      136. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      137. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      138. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      139. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      140. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      141. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      142. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      143. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      144. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      145. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      146. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      147. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      148. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      149. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      150. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      151. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      152. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      153. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      154. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      155. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      156. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      157. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      158. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      159. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      160. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      161. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      162. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      163. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      164. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      165. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      166. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      167. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      168. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      169. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      170. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      171. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      172. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      173. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      174. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      175. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      176. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      177. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      178. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      179. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      180. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      181. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      182. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      183. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      184. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      185. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      186. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      187. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      188. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      189. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      190. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      191. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      192. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      193. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      194. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      195. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      196. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      197. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      198. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      199. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      200. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      201. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      202. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      203. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      204. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      205. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      206. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      207. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      208. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      209. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      210. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      211. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      212. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      213. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      214. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      215. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      216. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      217. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      218. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      219. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      220. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      221. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      222. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      223. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      224. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      225. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      226. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      227. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      228. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      229. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      230. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      231. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      232. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      233. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      234. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      235. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      236. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      237. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      238. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      239. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      240. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      241. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      242. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      243. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      244. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      245. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      246. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      247. linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
      248. linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 4, 1) with arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
      249. linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
      250. linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
      251. linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
      252. linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
      253. linear OOA(256³, 16386, F₂₅₆, 4, 2) (dual of [(16386, 4), 65541, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256³, 65793, F₂₅₆, 4, 2) (dual of [(65793, 4), 263169, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(256³, 65793, F₂₅₆, 2, 2) (dual of [(65793, 2), 131583, 3]-NRT-code), using
        appending kth column [i] based on linear OA(256³, 65793, F₂₅₆, 2) (dual of [65793, 65790, 3]-code), using
        Hamming code H(3,256) [i]
      254. linear OOA(256⁴, 16386, F₂₅₆, 4, 3) (dual of [(16386, 4), 65540, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁴, 65537, F₂₅₆, 4, 3) (dual of [(65537, 4), 262144, 4]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
      255. linear OOA(256⁶, 16386, F₂₅₆, 4, 4) (dual of [(16386, 4), 65538, 5]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁶, 32640, F₂₅₆, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(256⁶, 65280, F₂₅₆, 4) (dual of [65280, 65274, 5]-code), using
        1 times truncation [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
      256. linear OOA(256¹⁹, 16386, F₂₅₆, 4, 9) (dual of [(16386, 4), 65525, 10]-NRT-code), using
        OOA 4-folding [i] based on linear OA(256¹⁹, 65544, F₂₅₆, 9) (dual of [65544, 65525, 10]-code), using
        constructionÂ X applied to C_e(8) âŠ‚ C_e(5) [i] based on
        linear OA(256¹⁷, 65536, F₂₅₆, 9) (dual of [65536, 65519, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [i]

(34, 34+9, large)-Net over F₁₂₈ — Digital

Digital (34, 43, large)-net over F₁₂₈, using

t-expansion [i] based on digital (32, 43, large)-net over F₁₂₈, using
- 1 times m-reduction [i] based on digital (32, 44, large)-net over F₁₂₈, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(34, 34+9, large)-Net in Base 128 — Upper bound on s

There is no (34, 43, large)-net in base 128, because

7 times m-reduction [i] would yield (34, 36, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (34, 34+9, s)-Nets in Base 128

(34, 34+9, 3145727)-Net over F128 — Constructive and digital

(34, 34+9, 4194815)-Net in Base 128 — Constructive

(34, 34+9, large)-Net over F128 — Digital

(34, 34+9, large)-Net in Base 128 — Upper bound on s

(34, 34+9, 3145727)-Net over F₁₂₈ — Constructive and digital

(34, 34+9, large)-Net over F₁₂₈ — Digital