Information on Result #547708
There is no linear OA(2213, 358, F2, 92) (dual of [358, 145, 93]-code), because construction Y1 would yield
- OA(2212, 300, S2, 92), but
- the linear programming bound shows that M ≥ 2484 132694 351399 471861 447697 940992 402712 231248 004226 234322 576635 442083 069406 167011 327832 607273 517056 / 377277 818302 855799 777736 052112 623275 > 2212 [i]
- linear OA(2145, 358, F2, 58) (dual of [358, 213, 59]-code), but
- discarding factors / shortening the dual code would yield linear OA(2145, 343, F2, 58) (dual of [343, 198, 59]-code), but
- the improved Johnson bound shows that N ≤ 7 839683 395577 661521 065550 956096 419139 602118 236678 534951 091663 < 2198 [i]
- discarding factors / shortening the dual code would yield linear OA(2145, 343, F2, 58) (dual of [343, 198, 59]-code), but
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(2214, 359, F2, 93) (dual of [359, 145, 94]-code) | [i] | Truncation | |
| 2 | No linear OOA(2214, 358, F2, 2, 93) (dual of [(358, 2), 502, 94]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2213, 358, F2, 2, 92) (dual of [(358, 2), 503, 93]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2213, 358, F2, 3, 92) (dual of [(358, 3), 861, 93]-NRT-code) | [i] | ||
| 5 | No linear OOA(2213, 358, F2, 4, 92) (dual of [(358, 4), 1219, 93]-NRT-code) | [i] | ||
| 6 | No linear OOA(2213, 358, F2, 5, 92) (dual of [(358, 5), 1577, 93]-NRT-code) | [i] | ||
| 7 | No linear OOA(2213, 358, F2, 6, 92) (dual of [(358, 6), 1935, 93]-NRT-code) | [i] | ||
| 8 | No linear OOA(2213, 358, F2, 7, 92) (dual of [(358, 7), 2293, 93]-NRT-code) | [i] | ||
| 9 | No linear OOA(2213, 358, F2, 8, 92) (dual of [(358, 8), 2651, 93]-NRT-code) | [i] | ||
| 10 | No digital (121, 213, 358)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |