Information on Result #547599
There is no linear OA(8157, 238, F8, 136) (dual of [238, 81, 137]-code), because residual code would yield OA(821, 101, S8, 17), but
- 1 times truncation [i] would yield OA(820, 100, S8, 16), but
- the linear programming bound shows that M ≥ 766 916854 670851 025894 998613 688320 / 621 810617 698353 > 820 [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(8158, 239, F8, 137) (dual of [239, 81, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(8159, 240, F8, 138) (dual of [240, 81, 139]-code) | [i] | ||
| 3 | No linear OA(8160, 241, F8, 139) (dual of [241, 81, 140]-code) | [i] | ||
| 4 | No linear OA(8161, 242, F8, 140) (dual of [242, 81, 141]-code) | [i] | ||
| 5 | No linear OA(8162, 243, F8, 141) (dual of [243, 81, 142]-code) | [i] | ||
| 6 | No linear OA(8163, 244, F8, 142) (dual of [244, 81, 143]-code) | [i] | ||
| 7 | No linear OA(8164, 245, F8, 143) (dual of [245, 81, 144]-code) | [i] | ||
| 8 | No linear OOA(8158, 238, F8, 2, 137) (dual of [(238, 2), 318, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(8159, 238, F8, 2, 138) (dual of [(238, 2), 317, 139]-NRT-code) | [i] | ||
| 10 | No linear OOA(8160, 238, F8, 2, 139) (dual of [(238, 2), 316, 140]-NRT-code) | [i] | ||
| 11 | No linear OOA(8161, 238, F8, 2, 140) (dual of [(238, 2), 315, 141]-NRT-code) | [i] | ||
| 12 | No linear OOA(8162, 238, F8, 2, 141) (dual of [(238, 2), 314, 142]-NRT-code) | [i] | ||
| 13 | No linear OOA(8163, 238, F8, 2, 142) (dual of [(238, 2), 313, 143]-NRT-code) | [i] | ||
| 14 | No linear OOA(8164, 238, F8, 2, 143) (dual of [(238, 2), 312, 144]-NRT-code) | [i] | ||
| 15 | No linear OOA(8157, 238, F8, 2, 136) (dual of [(238, 2), 319, 137]-NRT-code) | [i] | Depth Reduction | |
| 16 | No linear OOA(8157, 238, F8, 3, 136) (dual of [(238, 3), 557, 137]-NRT-code) | [i] | ||
| 17 | No digital (21, 157, 238)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 18 | No linear OA(8100, 257, F8, 85) (dual of [257, 157, 86]-code) | [i] | Construction Y1 (Bound) | |