Information on Result #547358
There is no linear OA(4221, 257, F4, 164) (dual of [257, 36, 165]-code), because residual code would yield OA(457, 92, S4, 41), but
- the linear programming bound shows that M ≥ 6 100582 649939 373494 201236 613796 043446 468174 965411 145692 768274 219008 / 286 854938 046996 694993 355683 683465 > 457 [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(4222, 258, F4, 165) (dual of [258, 36, 166]-code) | [i] | Truncation | |
| 2 | No linear OA(4223, 259, F4, 166) (dual of [259, 36, 167]-code) | [i] | ||
| 3 | No linear OA(4224, 260, F4, 167) (dual of [260, 36, 168]-code) | [i] | ||
| 4 | No linear OOA(4222, 257, F4, 2, 165) (dual of [(257, 2), 292, 166]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4223, 257, F4, 2, 166) (dual of [(257, 2), 291, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(4224, 257, F4, 2, 167) (dual of [(257, 2), 290, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(4221, 257, F4, 2, 164) (dual of [(257, 2), 293, 165]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4221, 257, F4, 3, 164) (dual of [(257, 3), 550, 165]-NRT-code) | [i] | ||
| 9 | No digital (57, 221, 257)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |