Information on Result #547761

There is no linear OA(3114, 181, F3, 71) (dual of [181, 67, 72]-code), because construction Y1 would yield
  1. OA(3113, 143, S3, 71), but
    • the linear programming bound shows that M ≥ 31 672520 199297 585243 899154 531146 784746 691310 342121 601962 325858 908470 456893 / 37 514198 689317 280000 > 3113 [i]
  2. OA(367, 181, S3, 38), but
    • discarding factors would yield OA(367, 175, S3, 38), but
      • the linear programming bound shows that M ≥ 387 999317 807943 805026 164281 984581 507597 966785 079804 265116 880208 641606 720469 396519 780352 / 3 893635 890543 207464 665118 176286 227992 932894 706751 830787 > 367 [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(3114, 181, F3, 2, 71) (dual of [(181, 2), 248, 72]-NRT-code) [i]Depth Reduction
2No linear OOA(3114, 181, F3, 3, 71) (dual of [(181, 3), 429, 72]-NRT-code) [i]
3No linear OOA(3114, 181, F3, 4, 71) (dual of [(181, 4), 610, 72]-NRT-code) [i]
4No linear OOA(3114, 181, F3, 5, 71) (dual of [(181, 5), 791, 72]-NRT-code) [i]
5No digital (43, 114, 181)-net over F3 [i]Extracting Embedded Orthogonal Array