Information on Result #547767

There is no linear OA(3121, 179, F3, 76) (dual of [179, 58, 77]-code), because construction Y1 would yield
  1. OA(3120, 147, S3, 76), but
    • the linear programming bound shows that M ≥ 69078 292689 709882 572905 172994 242151 837214 871842 231910 048557 184430 219838 603151 / 28 337998 861461 927055 > 3120 [i]
  2. OA(358, 179, S3, 32), but
    • discarding factors would yield OA(358, 173, S3, 32), but
      • the linear programming bound shows that M ≥ 47 314229 835710 776345 670615 418214 790563 428291 670976 086718 521800 / 9965 095822 320687 546955 148607 190123 > 358 [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(3121, 179, F3, 2, 76) (dual of [(179, 2), 237, 77]-NRT-code) [i]Depth Reduction
2No linear OOA(3121, 179, F3, 3, 76) (dual of [(179, 3), 416, 77]-NRT-code) [i]
3No linear OOA(3121, 179, F3, 4, 76) (dual of [(179, 4), 595, 77]-NRT-code) [i]
4No linear OOA(3121, 179, F3, 5, 76) (dual of [(179, 5), 774, 77]-NRT-code) [i]
5No digital (45, 121, 179)-net over F3 [i]Extracting Embedded Orthogonal Array