Information on Result #547415
There is no linear OA(4243, 454, F4, 172) (dual of [454, 211, 173]-code), because residual code would yield OA(471, 281, S4, 43), but
- the linear programming bound shows that M ≥ 373 183646 729416 144099 480364 087718 649481 545879 174441 862191 129687 019685 715860 929497 289195 520000 / 66 442053 478467 341276 388448 356669 192467 605369 216717 > 471 [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(4244, 455, F4, 173) (dual of [455, 211, 174]-code) | [i] | Truncation | |
| 2 | No linear OA(4245, 456, F4, 174) (dual of [456, 211, 175]-code) | [i] | ||
| 3 | No linear OA(4246, 457, F4, 175) (dual of [457, 211, 176]-code) | [i] | ||
| 4 | No linear OOA(4244, 454, F4, 2, 173) (dual of [(454, 2), 664, 174]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4245, 454, F4, 2, 174) (dual of [(454, 2), 663, 175]-NRT-code) | [i] | ||
| 6 | No linear OOA(4246, 454, F4, 2, 175) (dual of [(454, 2), 662, 176]-NRT-code) | [i] | ||
| 7 | No linear OOA(4243, 454, F4, 2, 172) (dual of [(454, 2), 665, 173]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4243, 454, F4, 3, 172) (dual of [(454, 3), 1119, 173]-NRT-code) | [i] | ||
| 9 | No digital (71, 243, 454)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |