Information on Result #547720
There is no linear OA(2245, 332, F2, 110) (dual of [332, 87, 111]-code), because construction Y1 would yield
- OA(2244, 300, S2, 110), but
- the linear programming bound shows that M ≥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2244 [i]
- OA(287, 332, S2, 32), but
- discarding factors would yield OA(287, 302, S2, 32), but
- the Rao or (dual) Hamming bound shows that M ≥ 161 699122 225452 699910 750634 > 287 [i]
- discarding factors would yield OA(287, 302, S2, 32), 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(2246, 333, F2, 111) (dual of [333, 87, 112]-code) | [i] | Truncation | |
| 2 | No linear OOA(2246, 332, F2, 2, 111) (dual of [(332, 2), 418, 112]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2248, 332, F2, 2, 113) (dual of [(332, 2), 416, 114]-NRT-code) | [i] | ||
| 4 | No linear OOA(2249, 332, F2, 2, 114) (dual of [(332, 2), 415, 115]-NRT-code) | [i] | ||
| 5 | No linear OOA(2250, 332, F2, 2, 115) (dual of [(332, 2), 414, 116]-NRT-code) | [i] | ||
| 6 | No linear OOA(2251, 332, F2, 2, 116) (dual of [(332, 2), 413, 117]-NRT-code) | [i] | ||
| 7 | No linear OOA(2252, 332, F2, 2, 117) (dual of [(332, 2), 412, 118]-NRT-code) | [i] | ||
| 8 | No linear OOA(2253, 332, F2, 2, 118) (dual of [(332, 2), 411, 119]-NRT-code) | [i] | ||
| 9 | No linear OOA(2254, 332, F2, 2, 119) (dual of [(332, 2), 410, 120]-NRT-code) | [i] | ||
| 10 | No linear OOA(2255, 332, F2, 2, 120) (dual of [(332, 2), 409, 121]-NRT-code) | [i] | ||
| 11 | No linear OOA(2256, 332, F2, 2, 121) (dual of [(332, 2), 408, 122]-NRT-code) | [i] | ||
| 12 | No linear OOA(2257, 332, F2, 2, 122) (dual of [(332, 2), 407, 123]-NRT-code) | [i] | ||
| 13 | No linear OOA(2258, 332, F2, 2, 123) (dual of [(332, 2), 406, 124]-NRT-code) | [i] | ||
| 14 | No linear OOA(2259, 332, F2, 2, 124) (dual of [(332, 2), 405, 125]-NRT-code) | [i] | ||
| 15 | No linear OOA(2260, 332, F2, 2, 125) (dual of [(332, 2), 404, 126]-NRT-code) | [i] | ||
| 16 | No linear OOA(2245, 332, F2, 2, 110) (dual of [(332, 2), 419, 111]-NRT-code) | [i] | Depth Reduction | |
| 17 | No linear OOA(2245, 332, F2, 3, 110) (dual of [(332, 3), 751, 111]-NRT-code) | [i] | ||
| 18 | No linear OOA(2245, 332, F2, 4, 110) (dual of [(332, 4), 1083, 111]-NRT-code) | [i] | ||
| 19 | No linear OOA(2245, 332, F2, 5, 110) (dual of [(332, 5), 1415, 111]-NRT-code) | [i] | ||
| 20 | No linear OOA(2245, 332, F2, 6, 110) (dual of [(332, 6), 1747, 111]-NRT-code) | [i] | ||
| 21 | No linear OOA(2245, 332, F2, 7, 110) (dual of [(332, 7), 2079, 111]-NRT-code) | [i] | ||
| 22 | No linear OOA(2245, 332, F2, 8, 110) (dual of [(332, 8), 2411, 111]-NRT-code) | [i] | ||
| 23 | No digital (135, 245, 332)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 24 | No linear OA(2246, 386, F2, 110) (dual of [386, 140, 111]-code) | [i] | Construction Y1 (Bound) | |