Information on Result #547714
There is no linear OA(2234, 332, F2, 104) (dual of [332, 98, 105]-code), because construction Y1 would yield
- OA(2233, 296, S2, 104), but
- the linear programming bound shows that M ≥ 40 441027 764911 159411 999678 250893 328460 000589 698723 782371 054222 923004 931887 671319 124733 067264 / 2499 525994 551277 812375 > 2233 [i]
- linear OA(298, 332, F2, 36) (dual of [332, 234, 37]-code), but
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-code), but
- the Johnson bound shows that N ≤ 1638 846907 564815 429866 669910 715625 391366 929534 207151 722672 384476 916602 < 2230 [i]
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-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(2235, 333, F2, 105) (dual of [333, 98, 106]-code) | [i] | Truncation | |
| 2 | No linear OOA(2235, 332, F2, 2, 105) (dual of [(332, 2), 429, 106]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2234, 332, F2, 2, 104) (dual of [(332, 2), 430, 105]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2234, 332, F2, 3, 104) (dual of [(332, 3), 762, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(2234, 332, F2, 4, 104) (dual of [(332, 4), 1094, 105]-NRT-code) | [i] | ||
| 6 | No linear OOA(2234, 332, F2, 5, 104) (dual of [(332, 5), 1426, 105]-NRT-code) | [i] | ||
| 7 | No linear OOA(2234, 332, F2, 6, 104) (dual of [(332, 6), 1758, 105]-NRT-code) | [i] | ||
| 8 | No linear OOA(2234, 332, F2, 7, 104) (dual of [(332, 7), 2090, 105]-NRT-code) | [i] | ||
| 9 | No linear OOA(2234, 332, F2, 8, 104) (dual of [(332, 8), 2422, 105]-NRT-code) | [i] | ||
| 10 | No digital (130, 234, 332)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 11 | No linear OA(2235, 396, F2, 104) (dual of [396, 161, 105]-code) | [i] | Construction Y1 (Bound) | |