Information on Result #547765

There is no linear OA(3120, 181, F3, 75) (dual of [181, 61, 76]-code), because construction Y1 would yield
  1. OA(3119, 147, S3, 75), but
    • the linear programming bound shows that M ≥ 16 137915 552723 745131 682214 391750 091116 522557 190679 736158 328855 711764 240731 / 23372 130007 496452 > 3119 [i]
  2. OA(361, 181, S3, 34), but
    • discarding factors would yield OA(361, 176, S3, 34), but
      • the linear programming bound shows that M ≥ 812 356626 791711 438639 003017 318488 339021 708011 289038 629210 828125 / 5801 809430 490682 982977 100374 687357 > 361 [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(3120, 181, F3, 2, 75) (dual of [(181, 2), 242, 76]-NRT-code) [i]Depth Reduction
2No linear OOA(3120, 181, F3, 3, 75) (dual of [(181, 3), 423, 76]-NRT-code) [i]
3No linear OOA(3120, 181, F3, 4, 75) (dual of [(181, 4), 604, 76]-NRT-code) [i]
4No linear OOA(3120, 181, F3, 5, 75) (dual of [(181, 5), 785, 76]-NRT-code) [i]
5No digital (45, 120, 181)-net over F3 [i]Extracting Embedded Orthogonal Array