Information on Result #547873
There is no linear OA(4136, 167, F4, 99) (dual of [167, 31, 100]-code), because construction Y1 would yield
- OA(4135, 149, S4, 99), but
- the linear programming bound shows that M ≥ 2 040610 487096 181427 758937 498317 933435 839690 422249 792187 355243 784188 300883 648114 289820 041216 / 970 822125 > 4135 [i]
- OA(431, 167, S4, 18), but
- the linear programming bound shows that M ≥ 10 709160 698850 412098 268143 898591 232000 / 2 251884 149854 892341 > 431 [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(4137, 168, F4, 100) (dual of [168, 31, 101]-code) | [i] | Truncation | |
| 2 | No linear OA(4138, 169, F4, 101) (dual of [169, 31, 102]-code) | [i] | ||
| 3 | No linear OOA(4137, 167, F4, 2, 100) (dual of [(167, 2), 197, 101]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(4138, 167, F4, 2, 101) (dual of [(167, 2), 196, 102]-NRT-code) | [i] | ||
| 5 | No linear OOA(4136, 167, F4, 2, 99) (dual of [(167, 2), 198, 100]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(4136, 167, F4, 3, 99) (dual of [(167, 3), 365, 100]-NRT-code) | [i] | ||
| 7 | No digital (37, 136, 167)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 8 | No linear OA(4137, 238, F4, 99) (dual of [238, 101, 100]-code) | [i] | Construction Y1 (Bound) | |