Information on Result #547318
There is no linear OA(4213, 291, F4, 156) (dual of [291, 78, 157]-code), because residual code would yield OA(457, 134, S4, 39), but
- the linear programming bound shows that M ≥ 2118 872152 947773 735205 614860 840104 993723 173522 547123 836257 668222 520389 144284 698869 497944 229365 678080 000000 / 96823 132929 101376 060431 157559 643789 049324 330608 249156 649224 680559 609039 > 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(4214, 292, F4, 157) (dual of [292, 78, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4215, 293, F4, 158) (dual of [293, 78, 159]-code) | [i] | ||
| 3 | No linear OA(4216, 294, F4, 159) (dual of [294, 78, 160]-code) | [i] | ||
| 4 | No linear OOA(4214, 291, F4, 2, 157) (dual of [(291, 2), 368, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4215, 291, F4, 2, 158) (dual of [(291, 2), 367, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4216, 291, F4, 2, 159) (dual of [(291, 2), 366, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4213, 291, F4, 2, 156) (dual of [(291, 2), 369, 157]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4213, 291, F4, 3, 156) (dual of [(291, 3), 660, 157]-NRT-code) | [i] | ||
| 9 | No digital (57, 213, 291)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |