Information on Result #547457
There is no linear OA(4248, 361, F4, 180) (dual of [361, 113, 181]-code), because residual code would yield OA(468, 180, S4, 45), but
- the linear programming bound shows that M ≥ 328494 790735 001198 305199 602445 532392 471737 863161 499929 581656 031112 774235 621273 901469 693549 435944 960000 000000 / 3 747617 146367 023709 191641 153229 380578 240235 288823 915002 005290 401803 > 468 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4249, 362, F4, 181) (dual of [362, 113, 182]-code) | [i] | Truncation | |
| 2 | No linear OA(4250, 363, F4, 182) (dual of [363, 113, 183]-code) | [i] | ||
| 3 | No linear OA(4251, 364, F4, 183) (dual of [364, 113, 184]-code) | [i] | ||
| 4 | No linear OOA(4249, 361, F4, 2, 181) (dual of [(361, 2), 473, 182]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4250, 361, F4, 2, 182) (dual of [(361, 2), 472, 183]-NRT-code) | [i] | ||
| 6 | No linear OOA(4251, 361, F4, 2, 183) (dual of [(361, 2), 471, 184]-NRT-code) | [i] | ||
| 7 | No linear OOA(4248, 361, F4, 2, 180) (dual of [(361, 2), 474, 181]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4248, 361, F4, 3, 180) (dual of [(361, 3), 835, 181]-NRT-code) | [i] | ||
| 9 | No digital (68, 248, 361)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |