Information on Result #546653
There is no linear OA(3147, 188, F3, 96) (dual of [188, 41, 97]-code), because residual code would yield OA(351, 91, S3, 32), but
- the linear programming bound shows that M ≥ 3 796003 121606 659684 644081 485270 254802 809922 702083 145243 272087 278428 845740 570091 586803 340207 313946 354006 591960 625547 / 1 756668 470243 430645 991636 297238 233510 101788 678484 940922 765709 380449 381903 813470 038571 507115 > 351 [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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3148, 189, F3, 97) (dual of [189, 41, 98]-code) | [i] | Truncation | |
| 2 | No linear OA(3149, 190, F3, 98) (dual of [190, 41, 99]-code) | [i] | ||
| 3 | No linear OOA(3148, 188, F3, 2, 97) (dual of [(188, 2), 228, 98]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3149, 188, F3, 2, 98) (dual of [(188, 2), 227, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(3147, 188, F3, 2, 96) (dual of [(188, 2), 229, 97]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3147, 188, F3, 3, 96) (dual of [(188, 3), 417, 97]-NRT-code) | [i] | ||
| 7 | No linear OOA(3147, 188, F3, 4, 96) (dual of [(188, 4), 605, 97]-NRT-code) | [i] | ||
| 8 | No linear OOA(3147, 188, F3, 5, 96) (dual of [(188, 5), 793, 97]-NRT-code) | [i] | ||
| 9 | No digital (51, 147, 188)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |