Information on Result #547603
There is no linear OA(8161, 415, F8, 136) (dual of [415, 254, 137]-code), because residual code would yield OA(825, 278, S8, 17), but
- 1 times truncation [i] would yield OA(824, 277, S8, 16), but
- the linear programming bound shows that M ≥ 78638 403871 838919 782431 803777 157693 440000 / 16 504446 602386 301789 > 824 [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(8162, 416, F8, 137) (dual of [416, 254, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(8163, 417, F8, 138) (dual of [417, 254, 139]-code) | [i] | ||
| 3 | No linear OA(8164, 418, F8, 139) (dual of [418, 254, 140]-code) | [i] | ||
| 4 | No linear OA(8165, 419, F8, 140) (dual of [419, 254, 141]-code) | [i] | ||
| 5 | No linear OA(8166, 420, F8, 141) (dual of [420, 254, 142]-code) | [i] | ||
| 6 | No linear OA(8167, 421, F8, 142) (dual of [421, 254, 143]-code) | [i] | ||
| 7 | No linear OA(8168, 422, F8, 143) (dual of [422, 254, 144]-code) | [i] | ||
| 8 | No linear OOA(8162, 415, F8, 2, 137) (dual of [(415, 2), 668, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8163, 415, F8, 2, 138) (dual of [(415, 2), 667, 139]-NRT-code) | [i] | ||
| 10 | No linear OOA(8164, 415, F8, 2, 139) (dual of [(415, 2), 666, 140]-NRT-code) | [i] | ||
| 11 | No linear OOA(8165, 415, F8, 2, 140) (dual of [(415, 2), 665, 141]-NRT-code) | [i] | ||
| 12 | No linear OOA(8166, 415, F8, 2, 141) (dual of [(415, 2), 664, 142]-NRT-code) | [i] | ||
| 13 | No linear OOA(8167, 415, F8, 2, 142) (dual of [(415, 2), 663, 143]-NRT-code) | [i] | ||
| 14 | No linear OOA(8168, 415, F8, 2, 143) (dual of [(415, 2), 662, 144]-NRT-code) | [i] | ||
| 15 | No linear OOA(8161, 415, F8, 2, 136) (dual of [(415, 2), 669, 137]-NRT-code) | [i] | Depth Reduction | |
| 16 | No linear OOA(8161, 415, F8, 3, 136) (dual of [(415, 3), 1084, 137]-NRT-code) | [i] | ||
| 17 | No digital (25, 161, 415)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |