Information on Result #547436
There is no linear OA(4246, 415, F4, 176) (dual of [415, 169, 177]-code), because residual code would yield OA(470, 238, S4, 44), but
- the linear programming bound shows that M ≥ 120510 936963 900302 789124 723066 073447 088671 101178 269184 854788 285280 658913 691603 030508 274974 720000 / 77708 615139 851578 435610 585674 497674 313378 544338 862201 > 470 [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(4247, 416, F4, 177) (dual of [416, 169, 178]-code) | [i] | Truncation | |
| 2 | No linear OA(4248, 417, F4, 178) (dual of [417, 169, 179]-code) | [i] | ||
| 3 | No linear OA(4249, 418, F4, 179) (dual of [418, 169, 180]-code) | [i] | ||
| 4 | No linear OOA(4247, 415, F4, 2, 177) (dual of [(415, 2), 583, 178]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4248, 415, F4, 2, 178) (dual of [(415, 2), 582, 179]-NRT-code) | [i] | ||
| 6 | No linear OOA(4249, 415, F4, 2, 179) (dual of [(415, 2), 581, 180]-NRT-code) | [i] | ||
| 7 | No linear OOA(4246, 415, F4, 2, 176) (dual of [(415, 2), 584, 177]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4246, 415, F4, 3, 176) (dual of [(415, 3), 999, 177]-NRT-code) | [i] | ||
| 9 | No digital (70, 246, 415)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |