Information on Result #547768

There is no linear OA(3123, 181, F3, 77) (dual of [181, 58, 78]-code), because construction Y1 would yield
  1. OA(3122, 149, S3, 77), but
    • the linear programming bound shows that M ≥ 67434 342292 992288 376762 260349 832237 588555 472017 770451 259524 588149 412506 954917 / 4 116623 563914 383665 > 3122 [i]
  2. OA(358, 181, 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(3123, 181, F3, 2, 77) (dual of [(181, 2), 239, 78]-NRT-code) [i]Depth Reduction
2No linear OOA(3123, 181, F3, 3, 77) (dual of [(181, 3), 420, 78]-NRT-code) [i]
3No linear OOA(3123, 181, F3, 4, 77) (dual of [(181, 4), 601, 78]-NRT-code) [i]
4No linear OOA(3123, 181, F3, 5, 77) (dual of [(181, 5), 782, 78]-NRT-code) [i]
5No digital (46, 123, 181)-net over F3 [i]Extracting Embedded Orthogonal Array