Information on Result #547238
There is no linear OA(4190, 251, F4, 140) (dual of [251, 61, 141]-code), because residual code would yield OA(450, 110, S4, 35), but
- the linear programming bound shows that M ≥ 2843 632588 461264 124732 153811 225362 179218 741807 134663 046707 045169 984379 030584 774721 441671 432589 217156 300800 / 1967 445154 431728 253949 288537 958066 067140 960836 153380 308963 321499 990743 635853 > 450 [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(4191, 252, F4, 141) (dual of [252, 61, 142]-code) | [i] | Truncation | |
| 2 | No linear OA(4192, 253, F4, 142) (dual of [253, 61, 143]-code) | [i] | ||
| 3 | No linear OA(4193, 254, F4, 143) (dual of [254, 61, 144]-code) | [i] | ||
| 4 | No linear OOA(4191, 251, F4, 2, 141) (dual of [(251, 2), 311, 142]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4192, 251, F4, 2, 142) (dual of [(251, 2), 310, 143]-NRT-code) | [i] | ||
| 6 | No linear OOA(4193, 251, F4, 2, 143) (dual of [(251, 2), 309, 144]-NRT-code) | [i] | ||
| 7 | No linear OOA(4190, 251, F4, 2, 140) (dual of [(251, 2), 312, 141]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4190, 251, F4, 3, 140) (dual of [(251, 3), 563, 141]-NRT-code) | [i] | ||
| 9 | No digital (50, 190, 251)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |