Information on Result #547756

There is no linear OA(3107, 199, F3, 66) (dual of [199, 92, 67]-code), because construction Y1 would yield
  1. OA(3106, 143, S3, 66), but
    • the linear programming bound shows that M ≥ 50584 630946 042848 451389 778465 029449 231952 748470 489372 922254 899547 818597 / 106 273880 037977 292025 > 3106 [i]
  2. OA(392, 199, S3, 56), but
    • discarding factors would yield OA(392, 150, S3, 56), but
      • the linear programming bound shows that M ≥ 380 530607 134695 199590 326105 296054 561976 304500 746203 230842 591578 312022 091639 435706 399387 387663 092379 / 4 623519 949937 639772 321756 933595 131069 999192 578955 859375 > 392 [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(3107, 199, F3, 2, 66) (dual of [(199, 2), 291, 67]-NRT-code) [i]Depth Reduction
2No linear OOA(3107, 199, F3, 3, 66) (dual of [(199, 3), 490, 67]-NRT-code) [i]
3No linear OOA(3107, 199, F3, 4, 66) (dual of [(199, 4), 689, 67]-NRT-code) [i]
4No linear OOA(3107, 199, F3, 5, 66) (dual of [(199, 5), 888, 67]-NRT-code) [i]
5No digital (41, 107, 199)-net over F3 [i]Extracting Embedded Orthogonal Array