Information on Result #547381
There is no linear OA(4227, 272, F4, 168) (dual of [272, 45, 169]-code), because residual code would yield OA(459, 103, S4, 42), but
- the linear programming bound shows that M ≥ 20 209278 630007 954817 311657 592716 406577 471235 077989 401051 636395 089582 131646 221319 183990 947510 747136 / 59 997456 042944 145499 206694 218235 767252 553003 337898 939171 700875 > 459 [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(4228, 273, F4, 169) (dual of [273, 45, 170]-code) | [i] | Truncation | |
| 2 | No linear OA(4229, 274, F4, 170) (dual of [274, 45, 171]-code) | [i] | ||
| 3 | No linear OA(4230, 275, F4, 171) (dual of [275, 45, 172]-code) | [i] | ||
| 4 | No linear OOA(4228, 272, F4, 2, 169) (dual of [(272, 2), 316, 170]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4229, 272, F4, 2, 170) (dual of [(272, 2), 315, 171]-NRT-code) | [i] | ||
| 6 | No linear OOA(4230, 272, F4, 2, 171) (dual of [(272, 2), 314, 172]-NRT-code) | [i] | ||
| 7 | No linear OOA(4227, 272, F4, 2, 168) (dual of [(272, 2), 317, 169]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4227, 272, F4, 3, 168) (dual of [(272, 3), 589, 169]-NRT-code) | [i] | ||
| 9 | No digital (59, 227, 272)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |