Information on Result #547771
There is no linear OA(3127, 178, F3, 80) (dual of [178, 51, 81]-code), because construction Y1 would yield
- OA(3126, 150, S3, 80), but
- the linear programming bound shows that M ≥ 1 744284 668385 163500 346306 269658 104769 929699 691581 439318 970712 105752 702784 / 1 186440 433087 > 3126 [i]
- OA(351, 178, S3, 28), but
- discarding factors would yield OA(351, 172, S3, 28), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 263924 665338 043697 613937 > 351 [i]
- discarding factors would yield OA(351, 172, 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(3127, 178, F3, 2, 80) (dual of [(178, 2), 229, 81]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3127, 178, F3, 3, 80) (dual of [(178, 3), 407, 81]-NRT-code) | [i] | ||
| 3 | No linear OOA(3127, 178, F3, 4, 80) (dual of [(178, 4), 585, 81]-NRT-code) | [i] | ||
| 4 | No linear OOA(3127, 178, F3, 5, 80) (dual of [(178, 5), 763, 81]-NRT-code) | [i] | ||
| 5 | No digital (47, 127, 178)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(397, 224, F3, 59) (dual of [224, 127, 60]-code) | [i] | Construction Y1 (Bound) | |