Information on Result #547470
There is no linear OA(4244, 251, F4, 184) (dual of [251, 7, 185]-code), because residual code would yield OA(460, 66, S4, 46), but
- the linear programming bound shows that M ≥ 340 282366 920938 463463 374607 431768 211456 / 235 > 460 [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4245, 252, F4, 185) (dual of [252, 7, 186]-code) | [i] | Truncation | |
| 2 | No linear OA(4246, 253, F4, 186) (dual of [253, 7, 187]-code) | [i] | ||
| 3 | No linear OA(4247, 254, F4, 187) (dual of [254, 7, 188]-code) | [i] | ||
| 4 | No linear OOA(4245, 251, F4, 2, 185) (dual of [(251, 2), 257, 186]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4246, 251, F4, 2, 186) (dual of [(251, 2), 256, 187]-NRT-code) | [i] | ||
| 6 | No linear OOA(4247, 251, F4, 2, 187) (dual of [(251, 2), 255, 188]-NRT-code) | [i] | ||
| 7 | No linear OOA(4248, 251, F4, 2, 188) (dual of [(251, 2), 254, 189]-NRT-code) | [i] | ||
| 8 | No linear OOA(4249, 251, F4, 2, 189) (dual of [(251, 2), 253, 190]-NRT-code) | [i] | ||
| 9 | No linear OOA(4250, 251, F4, 2, 190) (dual of [(251, 2), 252, 191]-NRT-code) | [i] | ||
| 10 | No linear OOA(4251, 251, F4, 2, 191) (dual of [(251, 2), 251, 192]-NRT-code) | [i] | ||
| 11 | No linear OOA(4252, 251, F4, 2, 192) (dual of [(251, 2), 250, 193]-NRT-code) | [i] | ||
| 12 | No linear OOA(4253, 251, F4, 2, 193) (dual of [(251, 2), 249, 194]-NRT-code) | [i] | ||
| 13 | No linear OOA(4254, 251, F4, 2, 194) (dual of [(251, 2), 248, 195]-NRT-code) | [i] | ||
| 14 | No linear OOA(4255, 251, F4, 2, 195) (dual of [(251, 2), 247, 196]-NRT-code) | [i] | ||
| 15 | No linear OOA(4256, 251, F4, 2, 196) (dual of [(251, 2), 246, 197]-NRT-code) | [i] | ||
| 16 | No linear OOA(4257, 251, F4, 2, 197) (dual of [(251, 2), 245, 198]-NRT-code) | [i] | ||
| 17 | No linear OOA(4258, 251, F4, 2, 198) (dual of [(251, 2), 244, 199]-NRT-code) | [i] | ||
| 18 | No linear OOA(4259, 251, F4, 2, 199) (dual of [(251, 2), 243, 200]-NRT-code) | [i] | ||
| 19 | No linear OOA(4260, 251, F4, 2, 200) (dual of [(251, 2), 242, 201]-NRT-code) | [i] | ||
| 20 | No linear OOA(4244, 251, F4, 2, 184) (dual of [(251, 2), 258, 185]-NRT-code) | [i] | Depth Reduction | |
| 21 | No linear OOA(4244, 251, F4, 3, 184) (dual of [(251, 3), 509, 185]-NRT-code) | [i] | ||
| 22 | No digital (60, 244, 251)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |