MinT - Information on Result #1226774

Information on Result #1226774

Digital (30, 38, 2101325)-net over F₆₄, using (u,Â u+v)-construction based on

digital (5, 9, 4175)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁹, 4175, F₆₄, 4, 4) (dual of [(4175, 4), 16691, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(64⁹, 4175, F₆₄, 3, 4) (dual of [(4175, 3), 12516, 5]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      3. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      4. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      5. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      6. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      7. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      8. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      9. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      10. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      11. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      12. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      13. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      14. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      15. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      16. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      17. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      18. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      19. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      20. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      21. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      22. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      23. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      24. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      25. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      26. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      27. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      28. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      29. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      30. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      31. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      32. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      33. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      34. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      35. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      36. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      37. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      38. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      39. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      40. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      41. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      42. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      43. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      44. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      45. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      46. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      47. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      48. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      49. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      50. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      51. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      52. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      53. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      54. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      55. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      56. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      57. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      58. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      59. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      60. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
      61. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
        appending 2 arbitrary columns [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      62. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code) (see above)
      63. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
      64. linear OOA(64⁵, 80, F₆₄, 3, 4) (dual of [(80, 3), 235, 5]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,235P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
digital (21, 29, 2097150)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64²⁹, 2097150, F₆₄, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(64²⁹, 8388600, F₆₄, 8) (dual of [8388600, 8388571, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

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

The following results depend on this result:

	Result		This result only	Method
1	Digital (43, 51, 4202650)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets