Information on Result #547764

There is no linear OA(3119, 187, F3, 74) (dual of [187, 68, 75]-code), because construction Y1 would yield
  1. OA(3118, 149, S3, 74), but
    • the linear programming bound shows that M ≥ 14631 013686 142997 953866 980562 476233 047154 143146 692997 967075 486096 911649 489501 / 62 737137 135696 970925 > 3118 [i]
  2. OA(368, 187, S3, 38), but
    • the linear programming bound shows that M ≥ 4 185011 256460 307952 313976 653889 690485 861995 490330 218229 391251 955691 449885 824042 401792 / 14773 934323 743575 783185 881134 593137 934301 575737 911449 > 368 [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(3119, 187, F3, 2, 74) (dual of [(187, 2), 255, 75]-NRT-code) [i]Depth Reduction
2No linear OOA(3119, 187, F3, 3, 74) (dual of [(187, 3), 442, 75]-NRT-code) [i]
3No linear OOA(3119, 187, F3, 4, 74) (dual of [(187, 4), 629, 75]-NRT-code) [i]
4No linear OOA(3119, 187, F3, 5, 74) (dual of [(187, 5), 816, 75]-NRT-code) [i]
5No digital (45, 119, 187)-net over F3 [i]Extracting Embedded Orthogonal Array
6No linear OA(3105, 224, F3, 64) (dual of [224, 119, 65]-code) [i]Construction Y1 (Bound)