Information on Result #547724
There is no linear OA(2248, 384, F2, 112) (dual of [384, 136, 113]-code), because construction Y1 would yield
- linear OA(2247, 332, F2, 112) (dual of [332, 85, 113]-code), but
- construction Y1 [i] would yield
- OA(2246, 302, S2, 112), but
- 2 times truncation [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]
- 2 times truncation [i] would yield OA(2244, 300, S2, 110), but
- linear OA(285, 332, F2, 30) (dual of [332, 247, 31]-code), but
- the Johnson bound shows that N ≤ 220 247871 551638 926977 652794 793575 888633 238636 124356 543746 403131 692235 320146 < 2247 [i]
- OA(2246, 302, S2, 112), but
- construction Y1 [i] would yield
- linear OA(2136, 384, F2, 52) (dual of [384, 248, 53]-code), but
- discarding factors / shortening the dual code would yield linear OA(2136, 374, F2, 52) (dual of [374, 238, 53]-code), but
- the improved Johnson bound shows that N ≤ 2 360702 811474 389063 749944 041391 364709 858504 534718 295956 994191 765553 370834 < 2238 [i]
- discarding factors / shortening the dual code would yield linear OA(2136, 374, F2, 52) (dual of [374, 238, 53]-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(2249, 385, F2, 113) (dual of [385, 136, 114]-code) | [i] | Truncation | |
| 2 | No linear OA(2250, 386, F2, 114) (dual of [386, 136, 115]-code) | [i] | ||
| 3 | No linear OA(2251, 387, F2, 115) (dual of [387, 136, 116]-code) | [i] | ||
| 4 | No linear OA(2252, 388, F2, 116) (dual of [388, 136, 117]-code) | [i] | ||
| 5 | No linear OA(2253, 389, F2, 117) (dual of [389, 136, 118]-code) | [i] | ||
| 6 | No linear OOA(2249, 384, F2, 2, 113) (dual of [(384, 2), 519, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 7 | No linear OOA(2250, 384, F2, 2, 114) (dual of [(384, 2), 518, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(2251, 384, F2, 2, 115) (dual of [(384, 2), 517, 116]-NRT-code) | [i] | ||
| 9 | No linear OOA(2252, 384, F2, 2, 116) (dual of [(384, 2), 516, 117]-NRT-code) | [i] | ||
| 10 | No linear OOA(2253, 384, F2, 2, 117) (dual of [(384, 2), 515, 118]-NRT-code) | [i] | ||
| 11 | No linear OOA(2254, 384, F2, 2, 118) (dual of [(384, 2), 514, 119]-NRT-code) | [i] | ||
| 12 | No linear OOA(2255, 384, F2, 2, 119) (dual of [(384, 2), 513, 120]-NRT-code) | [i] | ||
| 13 | No linear OOA(2248, 384, F2, 2, 112) (dual of [(384, 2), 520, 113]-NRT-code) | [i] | Depth Reduction | |
| 14 | No linear OOA(2248, 384, F2, 3, 112) (dual of [(384, 3), 904, 113]-NRT-code) | [i] | ||
| 15 | No linear OOA(2248, 384, F2, 4, 112) (dual of [(384, 4), 1288, 113]-NRT-code) | [i] | ||
| 16 | No linear OOA(2248, 384, F2, 5, 112) (dual of [(384, 5), 1672, 113]-NRT-code) | [i] | ||
| 17 | No linear OOA(2248, 384, F2, 6, 112) (dual of [(384, 6), 2056, 113]-NRT-code) | [i] | ||
| 18 | No linear OOA(2248, 384, F2, 7, 112) (dual of [(384, 7), 2440, 113]-NRT-code) | [i] | ||
| 19 | No linear OOA(2248, 384, F2, 8, 112) (dual of [(384, 8), 2824, 113]-NRT-code) | [i] | ||
| 20 | No digital (136, 248, 384)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |