Information on Result #547864

There is no linear OA(4126, 189, F4, 90) (dual of [189, 63, 91]-code), because construction Y1 would yield
  1. OA(4125, 148, S4, 90), but
    • the linear programming bound shows that M ≥ 136206 446948 908446 489058 171596 544731 344774 351426 147384 601300 725275 822927 378368 479690 899874 381824 / 71 216658 746873 765125 > 4125 [i]
  2. OA(463, 189, S4, 41), but
    • discarding factors would yield OA(463, 185, S4, 41), but
      • the linear programming bound shows that M ≥ 61 899957 150953 106035 135074 637879 046641 791483 715273 894502 688876 097802 046438 481549 501189 324800 / 720746 857989 042001 933213 860469 455977 050620 069897 655507 > 463 [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(4126, 189, F4, 2, 90) (dual of [(189, 2), 252, 91]-NRT-code) [i]Depth Reduction
2No linear OOA(4126, 189, F4, 3, 90) (dual of [(189, 3), 441, 91]-NRT-code) [i]
3No digital (36, 126, 189)-net over F4 [i]Extracting Embedded Orthogonal Array