Information on Result #546761
There is no linear OA(3189, 288, F3, 120) (dual of [288, 99, 121]-code), because residual code would yield OA(369, 167, S3, 40), but
- the linear programming bound shows that M ≥ 3 838665 658383 996413 263128 459526 338461 909456 293757 417139 423120 456477 969735 238321 348273 139503 831005 025192 377600 488198 751217 802922 834654 954870 122225 753549 660798 259207 409561 223364 519454 655647 580160 / 4311 115014 317421 270594 132571 568375 408760 296069 018114 037700 611694 533282 833176 081418 955437 885281 638335 483796 593997 602956 383645 120008 558634 695471 959296 440888 046791 > 369 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3190, 289, F3, 121) (dual of [289, 99, 122]-code) | [i] | Truncation | |
| 2 | No linear OA(3191, 290, F3, 122) (dual of [290, 99, 123]-code) | [i] | ||
| 3 | No linear OOA(3190, 288, F3, 2, 121) (dual of [(288, 2), 386, 122]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3191, 288, F3, 2, 122) (dual of [(288, 2), 385, 123]-NRT-code) | [i] | ||
| 5 | No linear OOA(3189, 288, F3, 2, 120) (dual of [(288, 2), 387, 121]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3189, 288, F3, 3, 120) (dual of [(288, 3), 675, 121]-NRT-code) | [i] | ||
| 7 | No linear OOA(3189, 288, F3, 4, 120) (dual of [(288, 4), 963, 121]-NRT-code) | [i] | ||
| 8 | No linear OOA(3189, 288, F3, 5, 120) (dual of [(288, 5), 1251, 121]-NRT-code) | [i] | ||
| 9 | No digital (69, 189, 288)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |