Information on Result #547769
There is no linear OA(3124, 176, F3, 78) (dual of [176, 52, 79]-code), because construction Y1 would yield
- OA(3123, 148, S3, 78), but
- the linear programming bound shows that M ≥ 7 262897 028362 273678 472870 511072 492435 452301 893929 213302 547823 936352 413873 / 144 349303 060703 > 3123 [i]
- OA(352, 176, S3, 28), but
- discarding factors would yield OA(352, 174, S3, 28), but
- the linear programming bound shows that M ≥ 4 161951 615411 252453 824540 942433 981968 425781 250000 / 620319 051805 227761 533237 > 352 [i]
- discarding factors would yield OA(352, 174, S3, 28), 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(3124, 176, F3, 2, 78) (dual of [(176, 2), 228, 79]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3124, 176, F3, 3, 78) (dual of [(176, 3), 404, 79]-NRT-code) | [i] | ||
| 3 | No linear OOA(3124, 176, F3, 4, 78) (dual of [(176, 4), 580, 79]-NRT-code) | [i] | ||
| 4 | No linear OOA(3124, 176, F3, 5, 78) (dual of [(176, 5), 756, 79]-NRT-code) | [i] | ||
| 5 | No digital (46, 124, 176)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |