Information on Result #546435
There is no linear OA(2197, 214, F2, 98) (dual of [214, 17, 99]-code), because residual code would yield OA(299, 115, S2, 49), but
- 1 times truncation [i] would yield OA(298, 114, S2, 48), but
- the linear programming bound shows that M ≥ 141449 524575 866749 536608 130468 675584 / 431375 > 298 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2198, 215, F2, 99) (dual of [215, 17, 100]-code) | [i] | Truncation | |
| 2 | No linear OOA(2198, 214, F2, 2, 99) (dual of [(214, 2), 230, 100]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2197, 214, F2, 2, 98) (dual of [(214, 2), 231, 99]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2197, 214, F2, 3, 98) (dual of [(214, 3), 445, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(2197, 214, F2, 4, 98) (dual of [(214, 4), 659, 99]-NRT-code) | [i] | ||
| 6 | No linear OOA(2197, 214, F2, 5, 98) (dual of [(214, 5), 873, 99]-NRT-code) | [i] | ||
| 7 | No linear OOA(2197, 214, F2, 6, 98) (dual of [(214, 6), 1087, 99]-NRT-code) | [i] | ||
| 8 | No linear OOA(2197, 214, F2, 7, 98) (dual of [(214, 7), 1301, 99]-NRT-code) | [i] | ||
| 9 | No linear OOA(2197, 214, F2, 8, 98) (dual of [(214, 8), 1515, 99]-NRT-code) | [i] | ||
| 10 | No digital (99, 197, 214)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |