Information on Result #547323
There is no linear OA(4218, 372, F4, 156) (dual of [372, 154, 157]-code), because residual code would yield OA(462, 215, S4, 39), but
- the linear programming bound shows that M ≥ 12718 083503 539266 529007 190946 224090 701310 717998 449746 183117 383672 455579 566080 / 595 821431 971093 361396 591608 721211 764591 > 462 [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(4219, 373, F4, 157) (dual of [373, 154, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4220, 374, F4, 158) (dual of [374, 154, 159]-code) | [i] | ||
| 3 | No linear OA(4221, 375, F4, 159) (dual of [375, 154, 160]-code) | [i] | ||
| 4 | No linear OOA(4219, 372, F4, 2, 157) (dual of [(372, 2), 525, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4220, 372, F4, 2, 158) (dual of [(372, 2), 524, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4221, 372, F4, 2, 159) (dual of [(372, 2), 523, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4218, 372, F4, 2, 156) (dual of [(372, 2), 526, 157]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4218, 372, F4, 3, 156) (dual of [(372, 3), 898, 157]-NRT-code) | [i] | ||
| 9 | No digital (62, 218, 372)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |