Information on Result #547792

There is no linear OA(3142, 156, F3, 94) (dual of [156, 14, 95]-code), because construction Y1 would yield
  1. OA(3141, 150, S3, 94), but
    • the linear programming bound shows that M ≥ 2 507699 731904 749483 156305 303283 721699 486095 458197 011266 969583 191489 627021 / 107749 > 3141 [i]
  2. OA(314, 156, S3, 6), but

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 OA(3143, 157, F3, 95) (dual of [157, 14, 96]-code) [i]Truncation
2No linear OA(3144, 158, F3, 96) (dual of [158, 14, 97]-code) [i]
3No linear OA(3145, 159, F3, 97) (dual of [159, 14, 98]-code) [i]
4No linear OA(3146, 160, F3, 98) (dual of [160, 14, 99]-code) [i]
5No linear OOA(3143, 156, F3, 2, 95) (dual of [(156, 2), 169, 96]-NRT-code) [i]m-Reduction for OOAs
6No linear OOA(3144, 156, F3, 2, 96) (dual of [(156, 2), 168, 97]-NRT-code) [i]
7No linear OOA(3145, 156, F3, 2, 97) (dual of [(156, 2), 167, 98]-NRT-code) [i]
8No linear OOA(3146, 156, F3, 2, 98) (dual of [(156, 2), 166, 99]-NRT-code) [i]
9No linear OOA(3142, 156, F3, 2, 94) (dual of [(156, 2), 170, 95]-NRT-code) [i]Depth Reduction
10No linear OOA(3142, 156, F3, 3, 94) (dual of [(156, 3), 326, 95]-NRT-code) [i]
11No linear OOA(3142, 156, F3, 4, 94) (dual of [(156, 4), 482, 95]-NRT-code) [i]
12No linear OOA(3142, 156, F3, 5, 94) (dual of [(156, 5), 638, 95]-NRT-code) [i]
13No digital (48, 142, 156)-net over F3 [i]Extracting Embedded Orthogonal Array
14No linear OA(3143, 168, F3, 94) (dual of [168, 25, 95]-code) [i]Construction Y1 (Bound)