Information on Result #547135
There is no linear OA(4144, 242, F4, 104) (dual of [242, 98, 105]-code), because residual code would yield OA(440, 137, S4, 26), but
- the linear programming bound shows that M ≥ 482 543072 349145 294988 866520 488882 831179 139598 254080 / 392 638906 322982 186151 177303 > 440 [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(4145, 243, F4, 105) (dual of [243, 98, 106]-code) | [i] | Truncation | |
| 2 | No linear OA(4146, 244, F4, 106) (dual of [244, 98, 107]-code) | [i] | ||
| 3 | No linear OA(4147, 245, F4, 107) (dual of [245, 98, 108]-code) | [i] | ||
| 4 | No linear OOA(4145, 242, F4, 2, 105) (dual of [(242, 2), 339, 106]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4146, 242, F4, 2, 106) (dual of [(242, 2), 338, 107]-NRT-code) | [i] | ||
| 6 | No linear OOA(4147, 242, F4, 2, 107) (dual of [(242, 2), 337, 108]-NRT-code) | [i] | ||
| 7 | No linear OOA(4144, 242, F4, 2, 104) (dual of [(242, 2), 340, 105]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4144, 242, F4, 3, 104) (dual of [(242, 3), 582, 105]-NRT-code) | [i] | ||
| 9 | No digital (40, 144, 242)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(4106, 250, F4, 74) (dual of [250, 144, 75]-code) | [i] | Construction Y1 (Bound) | |