Information on Result #547711
There is no linear OA(2224, 348, F2, 98) (dual of [348, 124, 99]-code), because construction Y1 would yield
- OA(2223, 300, S2, 98), but
- the linear programming bound shows that M ≥ 1 797227 776840 883681 896516 291018 079602 556004 736527 384481 376471 307374 972535 986485 205069 933364 379648 / 112622 624143 760877 566730 935625 > 2223 [i]
- linear OA(2124, 348, F2, 48) (dual of [348, 224, 49]-code), but
- discarding factors / shortening the dual code would yield linear OA(2124, 332, F2, 48) (dual of [332, 208, 49]-code), but
- the improved Johnson bound shows that N ≤ 1985 666223 770950 387579 854572 849250 190195 414082 522040 623254 891664 < 2208 [i]
- discarding factors / shortening the dual code would yield linear OA(2124, 332, F2, 48) (dual of [332, 208, 49]-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(2225, 349, F2, 99) (dual of [349, 124, 100]-code) | [i] | Truncation | |
| 2 | No linear OOA(2225, 348, F2, 2, 99) (dual of [(348, 2), 471, 100]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2224, 348, F2, 2, 98) (dual of [(348, 2), 472, 99]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2224, 348, F2, 3, 98) (dual of [(348, 3), 820, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(2224, 348, F2, 4, 98) (dual of [(348, 4), 1168, 99]-NRT-code) | [i] | ||
| 6 | No linear OOA(2224, 348, F2, 5, 98) (dual of [(348, 5), 1516, 99]-NRT-code) | [i] | ||
| 7 | No linear OOA(2224, 348, F2, 6, 98) (dual of [(348, 6), 1864, 99]-NRT-code) | [i] | ||
| 8 | No linear OOA(2224, 348, F2, 7, 98) (dual of [(348, 7), 2212, 99]-NRT-code) | [i] | ||
| 9 | No linear OOA(2224, 348, F2, 8, 98) (dual of [(348, 8), 2560, 99]-NRT-code) | [i] | ||
| 10 | No digital (126, 224, 348)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |