Information on Result #547721
There is no linear OA(2246, 386, F2, 110) (dual of [386, 140, 111]-code), because construction Y1 would yield
- linear OA(2245, 332, F2, 110) (dual of [332, 87, 111]-code), but
- construction Y1 [i] 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
- OA(2244, 300, S2, 110), but
- construction Y1 [i] would yield
- linear OA(2140, 386, F2, 54) (dual of [386, 246, 55]-code), but
- discarding factors / shortening the dual code would yield linear OA(2140, 376, F2, 54) (dual of [376, 236, 55]-code), but
- the improved Johnson bound shows that N ≤ 638271 859848 635367 775356 676031 149307 988937 824926 330314 504342 114737 011555 < 2236 [i]
- discarding factors / shortening the dual code would yield linear OA(2140, 376, F2, 54) (dual of [376, 236, 55]-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(2247, 387, F2, 111) (dual of [387, 140, 112]-code) | [i] | Truncation | |
| 2 | No linear OOA(2247, 386, F2, 2, 111) (dual of [(386, 2), 525, 112]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2246, 386, F2, 2, 110) (dual of [(386, 2), 526, 111]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2246, 386, F2, 3, 110) (dual of [(386, 3), 912, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(2246, 386, F2, 4, 110) (dual of [(386, 4), 1298, 111]-NRT-code) | [i] | ||
| 6 | No linear OOA(2246, 386, F2, 5, 110) (dual of [(386, 5), 1684, 111]-NRT-code) | [i] | ||
| 7 | No linear OOA(2246, 386, F2, 6, 110) (dual of [(386, 6), 2070, 111]-NRT-code) | [i] | ||
| 8 | No linear OOA(2246, 386, F2, 7, 110) (dual of [(386, 7), 2456, 111]-NRT-code) | [i] | ||
| 9 | No linear OOA(2246, 386, F2, 8, 110) (dual of [(386, 8), 2842, 111]-NRT-code) | [i] | ||
| 10 | No digital (136, 246, 386)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |