MinT - Information on Result #3279492

Information on Result #3279492

(97, 109, 7174494)-net in base 27, using 27¹ times duplication based on (96, 108, 7174494)-net in base 27, using

base change [i] based on digital (69, 81, 7174494)-net over F₈₁, using
- 81¹ times duplication [i] based on digital (68, 80, 7174494)-net over F₈₁, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 0, 88574)-net over F₈₁, using
      - s-reduction based on digital (0, 0, s)-net over F₈₁ for arbitrarily large s, using
        arbitrary set of 81⁰ points [i]
    2. digital (0, 0, 88574)-net over F₈₁ (see above)
    3. digital (0, 0, 88574)-net over F₈₁ (see above)
    4. digital (0, 0, 88574)-net over F₈₁ (see above)
    5. digital (0, 0, 88574)-net over F₈₁ (see above)
    6. digital (0, 0, 88574)-net over F₈₁ (see above)
    7. digital (0, 0, 88574)-net over F₈₁ (see above)
    8. digital (0, 0, 88574)-net over F₈₁ (see above)
    9. digital (0, 0, 88574)-net over F₈₁ (see above)
    10. digital (0, 0, 88574)-net over F₈₁ (see above)
    11. digital (0, 0, 88574)-net over F₈₁ (see above)
    12. digital (0, 0, 88574)-net over F₈₁ (see above)
    13. digital (0, 0, 88574)-net over F₈₁ (see above)
    14. digital (0, 0, 88574)-net over F₈₁ (see above)
    15. digital (0, 0, 88574)-net over F₈₁ (see above)
    16. digital (0, 0, 88574)-net over F₈₁ (see above)
    17. digital (0, 0, 88574)-net over F₈₁ (see above)
    18. digital (0, 0, 88574)-net over F₈₁ (see above)
    19. digital (0, 0, 88574)-net over F₈₁ (see above)
    20. digital (0, 0, 88574)-net over F₈₁ (see above)
    21. digital (0, 0, 88574)-net over F₈₁ (see above)
    22. digital (0, 0, 88574)-net over F₈₁ (see above)
    23. digital (0, 0, 88574)-net over F₈₁ (see above)
    24. digital (0, 0, 88574)-net over F₈₁ (see above)
    25. digital (0, 0, 88574)-net over F₈₁ (see above)
    26. digital (0, 0, 88574)-net over F₈₁ (see above)
    27. digital (0, 0, 88574)-net over F₈₁ (see above)
    28. digital (0, 0, 88574)-net over F₈₁ (see above)
    29. digital (0, 0, 88574)-net over F₈₁ (see above)
    30. digital (0, 0, 88574)-net over F₈₁ (see above)
    31. digital (0, 0, 88574)-net over F₈₁ (see above)
    32. digital (0, 0, 88574)-net over F₈₁ (see above)
    33. digital (0, 0, 88574)-net over F₈₁ (see above)
    34. digital (0, 0, 88574)-net over F₈₁ (see above)
    35. digital (0, 0, 88574)-net over F₈₁ (see above)
    36. digital (0, 0, 88574)-net over F₈₁ (see above)
    37. digital (0, 0, 88574)-net over F₈₁ (see above)
    38. digital (0, 0, 88574)-net over F₈₁ (see above)
    39. digital (0, 0, 88574)-net over F₈₁ (see above)
    40. digital (0, 0, 88574)-net over F₈₁ (see above)
    41. digital (0, 0, 88574)-net over F₈₁ (see above)
    42. digital (0, 0, 88574)-net over F₈₁ (see above)
    43. digital (0, 0, 88574)-net over F₈₁ (see above)
    44. digital (0, 0, 88574)-net over F₈₁ (see above)
    45. digital (0, 0, 88574)-net over F₈₁ (see above)
    46. digital (0, 0, 88574)-net over F₈₁ (see above)
    47. digital (0, 0, 88574)-net over F₈₁ (see above)
    48. digital (0, 0, 88574)-net over F₈₁ (see above)
    49. digital (0, 0, 88574)-net over F₈₁ (see above)
    50. digital (0, 0, 88574)-net over F₈₁ (see above)
    51. digital (0, 0, 88574)-net over F₈₁ (see above)
    52. digital (0, 0, 88574)-net over F₈₁ (see above)
    53. digital (0, 0, 88574)-net over F₈₁ (see above)
    54. digital (0, 0, 88574)-net over F₈₁ (see above)
    55. digital (0, 0, 88574)-net over F₈₁ (see above)
    56. digital (0, 0, 88574)-net over F₈₁ (see above)
    57. digital (0, 0, 88574)-net over F₈₁ (see above)
    58. digital (0, 0, 88574)-net over F₈₁ (see above)
    59. digital (0, 0, 88574)-net over F₈₁ (see above)
    60. digital (0, 0, 88574)-net over F₈₁ (see above)
    61. digital (0, 0, 88574)-net over F₈₁ (see above)
    62. digital (0, 0, 88574)-net over F₈₁ (see above)
    63. digital (0, 0, 88574)-net over F₈₁ (see above)
    64. digital (0, 0, 88574)-net over F₈₁ (see above)
    65. digital (0, 0, 88574)-net over F₈₁ (see above)
    66. digital (0, 0, 88574)-net over F₈₁ (see above)
    67. digital (0, 0, 88574)-net over F₈₁ (see above)
    68. digital (0, 0, 88574)-net over F₈₁ (see above)
    69. digital (0, 0, 88574)-net over F₈₁ (see above)
    70. digital (0, 1, 88574)-net over F₈₁, using
      - s-reduction based on digital (0, 1, s)-net over F₈₁ for arbitrarily large s, using
        construction for strength kÂ =Â 1 [i]
    71. digital (0, 1, 88574)-net over F₈₁ (see above)
    72. digital (0, 1, 88574)-net over F₈₁ (see above)
    73. digital (0, 1, 88574)-net over F₈₁ (see above)
    74. digital (0, 1, 88574)-net over F₈₁ (see above)
    75. digital (0, 1, 88574)-net over F₈₁ (see above)
    76. digital (2, 4, 88574)-net over F₈₁, using
      - s-reduction based on digital (2, 4, 538084)-net over F₈₁, using
        kÂ =Â 2 construction [i]
    77. digital (2, 4, 88574)-net over F₈₁ (see above)
    78. digital (3, 6, 88574)-net over F₈₁, using
      - s-reduction based on digital (3, 6, 538248)-net over F₈₁, using
        net defined by OOA [i] based on linear OOA(81⁶, 538248, F₈₁, 3, 3) (dual of [(538248, 3), 1614738, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(81⁶, 538248, F₈₁, 2, 3) (dual of [(538248, 2), 1076490, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁶, 538248, F₈₁, 3) (dual of [538248, 538242, 4]-code or 538248-cap in PG(5,81)), using
        large caps in PG(5,Â b) [i]
    79. digital (6, 10, 88574)-net over F₈₁, using
      - s-reduction based on digital (6, 10, 265722)-net over F₈₁, using
        net defined by OOA [i] based on linear OOA(81¹⁰, 265722, F₈₁, 4, 4) (dual of [(265722, 4), 1062878, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(81¹⁰, 531444, F₈₁, 4) (dual of [531444, 531434, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(81¹⁰, 531441, F₈₁, 4) (dual of [531441, 531431, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(81⁷, 531441, F₈₁, 3) (dual of [531441, 531434, 4]-code or 531441-cap in PG(6,81)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
    80. digital (10, 16, 88574)-net over F₈₁, using
      - s-reduction based on digital (10, 16, 177148)-net over F₈₁, using
        net defined by OOA [i] based on linear OOA(81¹⁶, 177148, F₈₁, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
        OA 3-folding and stacking [i] based on linear OA(81¹⁶, 531444, F₈₁, 6) (dual of [531444, 531428, 7]-code), using
        constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(81¹⁶, 531441, F₈₁, 6) (dual of [531441, 531425, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(81¹³, 531441, F₈₁, 5) (dual of [531441, 531428, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code) (see above)
    81. digital (22, 34, 88574)-net over F₈₁, using
      - net defined by OOA [i] based on linear OOA(81³⁴, 88574, F₈₁, 12, 12) (dual of [(88574, 12), 1062854, 13]-NRT-code), using
        OA 6-folding and stacking [i] based on linear OA(81³⁴, 531444, F₈₁, 12) (dual of [531444, 531410, 13]-code), using
        constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(81³⁴, 531441, F₈₁, 12) (dual of [531441, 531407, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(81³¹, 531441, F₈₁, 11) (dual of [531441, 531410, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code) (see above)

Mode: Constructive.

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.