Information on Result #547204
There is no linear OA(4178, 222, F4, 132) (dual of [222, 44, 133]-code), because residual code would yield OA(446, 89, S4, 33), but
- the linear programming bound shows that M ≥ 159948 754090 845526 538000 065296 234178 559990 299122 417191 613523 054637 510362 523087 608926 611865 440230 434765 845983 597818 865036 995130 058350 788608 / 31 655830 017094 855639 908154 532004 566126 868766 376087 543277 919844 313859 261385 645064 532693 335140 575232 262538 565325 > 446 [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(4179, 223, F4, 133) (dual of [223, 44, 134]-code) | [i] | Truncation | |
| 2 | No linear OA(4180, 224, F4, 134) (dual of [224, 44, 135]-code) | [i] | ||
| 3 | No linear OA(4181, 225, F4, 135) (dual of [225, 44, 136]-code) | [i] | ||
| 4 | No linear OOA(4179, 222, F4, 2, 133) (dual of [(222, 2), 265, 134]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4180, 222, F4, 2, 134) (dual of [(222, 2), 264, 135]-NRT-code) | [i] | ||
| 6 | No linear OOA(4181, 222, F4, 2, 135) (dual of [(222, 2), 263, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(4178, 222, F4, 2, 132) (dual of [(222, 2), 266, 133]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4178, 222, F4, 3, 132) (dual of [(222, 3), 488, 133]-NRT-code) | [i] | ||
| 9 | No digital (46, 178, 222)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |