Information on Result #547380
There is no linear OA(4226, 257, F4, 168) (dual of [257, 31, 169]-code), because residual code would yield OA(458, 88, S4, 42), but
- the linear programming bound shows that M ≥ 158 237175 107336 529531 271038 987459 138072 539269 830656 314178 535424 / 1500 577564 280935 407980 323611 > 458 [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(4227, 258, F4, 169) (dual of [258, 31, 170]-code) | [i] | Truncation | |
| 2 | No linear OA(4228, 259, F4, 170) (dual of [259, 31, 171]-code) | [i] | ||
| 3 | No linear OA(4229, 260, F4, 171) (dual of [260, 31, 172]-code) | [i] | ||
| 4 | No linear OOA(4227, 257, F4, 2, 169) (dual of [(257, 2), 287, 170]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4228, 257, F4, 2, 170) (dual of [(257, 2), 286, 171]-NRT-code) | [i] | ||
| 6 | No linear OOA(4229, 257, F4, 2, 171) (dual of [(257, 2), 285, 172]-NRT-code) | [i] | ||
| 7 | No linear OOA(4226, 257, F4, 2, 168) (dual of [(257, 2), 288, 169]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4226, 257, F4, 3, 168) (dual of [(257, 3), 545, 169]-NRT-code) | [i] | ||
| 9 | No digital (58, 226, 257)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |