Information on Result #547763

There is no linear OA(3117, 184, F3, 73) (dual of [184, 67, 74]-code), because construction Y1 would yield
  1. OA(3116, 146, S3, 73), but
    • the linear programming bound shows that M ≥ 4429 247306 617760 489204 086593 334014 244245 698002 651783 020636 205319 885138 080839 / 177 060239 926994 878648 > 3116 [i]
  2. OA(367, 184, 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(3117, 184, F3, 2, 73) (dual of [(184, 2), 251, 74]-NRT-code) [i]Depth Reduction
2No linear OOA(3117, 184, F3, 3, 73) (dual of [(184, 3), 435, 74]-NRT-code) [i]
3No linear OOA(3117, 184, F3, 4, 73) (dual of [(184, 4), 619, 74]-NRT-code) [i]
4No linear OOA(3117, 184, F3, 5, 73) (dual of [(184, 5), 803, 74]-NRT-code) [i]
5No digital (44, 117, 184)-net over F3 [i]Extracting Embedded Orthogonal Array