MinT - Best Known (15−5, 15, s)-Nets in Base 81

Best Known (15−5, 15, s)-Nets in Base 81

(15−5, 15, 269082)-Net over F₈₁ — Constructive and digital

Digital (10, 15, 269082)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81¹⁵, 269082, F₈₁, 5, 5) (dual of [(269082, 5), 1345395, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(81¹⁵, 269082, F₈₁, 4, 5) (dual of [(269082, 4), 1076313, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 4, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
    2. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    3. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    4. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    5. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    6. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    7. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    8. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    9. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    10. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    11. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    12. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    13. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    14. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    15. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    16. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    17. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    18. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    19. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    20. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    21. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    22. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    23. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    24. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    25. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    26. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    27. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    28. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    29. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    30. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    31. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    32. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    33. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    34. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    35. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    36. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    37. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    38. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    39. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    40. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    41. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    42. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    43. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    44. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    45. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    46. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    47. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    48. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    49. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    50. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    51. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    52. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    53. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    54. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    55. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    56. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    57. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    58. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    59. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    60. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    61. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    62. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    63. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    64. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    65. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    66. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    67. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    68. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    69. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    70. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    71. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    72. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    73. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    74. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    75. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    76. linear OOA(81⁰, 3322, F₈₁, 4, 0) (dual of [(3322, 4), 13288, 1]-NRT-code) (see above)
    77. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 4, 1) with arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
    78. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code) (see above)
    79. linear OOA(81¹, 3322, F₈₁, 4, 1) (dual of [(3322, 4), 13287, 2]-NRT-code) (see above)
    80. linear OOA(81³, 3322, F₈₁, 4, 2) (dual of [(3322, 4), 13285, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 4, 2) (dual of [(6643, 4), 26569, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
    81. linear OOA(81⁹, 3322, F₈₁, 4, 5) (dual of [(3322, 4), 13279, 6]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(81², 82, F₈₁, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;326,81) [i]
        linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]

(15−5, 15, 531603)-Net over F₈₁ — Digital

Digital (10, 15, 531603)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81¹⁵, 531603, F₈₁, 5, 5) (dual of [(531603, 5), 2658000, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(81¹⁵, 531603, F₈₁, 4, 5) (dual of [(531603, 4), 2126397, 6]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(81¹⁵, 531603, F₈₁, 5) (dual of [531603, 531588, 6]-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
      2. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      3. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      4. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      5. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      6. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      7. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      8. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      9. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      10. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      11. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      12. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      13. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      14. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      15. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      16. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      17. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      18. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      19. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      20. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      21. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      22. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      23. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      24. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      25. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      26. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      27. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      28. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      29. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      30. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      31. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      32. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      33. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      34. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      35. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      36. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      37. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      38. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      39. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      40. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      41. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      42. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      43. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      44. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      45. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      46. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      47. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      48. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      49. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      50. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      51. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      52. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      53. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      54. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      55. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      56. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      57. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      58. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      59. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      60. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      61. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      62. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      63. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      64. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      65. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      66. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      67. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      68. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      69. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      70. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      71. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      72. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      73. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      74. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      75. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      76. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
      77. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
      78. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code) (see above)
      79. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code) (see above)
      80. linear OA(81³, 6563, F₈₁, 2) (dual of [6563, 6560, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
      81. linear OA(81⁹, 6563, F₈₁, 5) (dual of [6563, 6554, 6]-code), using
        (u,Â u+v)-construction [i] based on
        linear OA(81², 82, F₈₁, 2) (dual of [82, 80, 3]-code or 82-arc in PG(1,81)), using
        extended Reedâ€“Solomon code RS_e(80,81) [i]
        Hamming code H(2,81) [i]
        linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]

(15−5, 15, large)-Net in Base 81 — Upper bound on s

There is no (10, 15, large)-net in base 81, because

3 times m-reduction [i] would yield (10, 12, large)-net in base 81, but
- mutually orthogonal hypercube bound [i]

Best Known (15−5, 15, s)-Nets in Base 81

(15−5, 15, 269082)-Net over F81 — Constructive and digital

(15−5, 15, 531603)-Net over F81 — Digital

(15−5, 15, large)-Net in Base 81 — Upper bound on s

(15−5, 15, 269082)-Net over F₈₁ — Constructive and digital

(15−5, 15, 531603)-Net over F₈₁ — Digital