Information on Result #547360
There is no linear OA(4223, 290, F4, 164) (dual of [290, 67, 165]-code), because residual code would yield OA(459, 125, S4, 41), but
- the linear programming bound shows that M ≥ 6 098659 704705 486904 667441 402011 989050 548288 910427 912825 765842 283670 760248 415348 522730 039189 577335 282788 475369 967101 883338 375933 306396 897634 126855 141698 525692 111751 859853 590528 / 17 865783 539531 952003 937094 580988 623442 037272 256331 005047 247373 356459 142621 652981 139301 072409 181322 127802 625025 609129 027701 857126 610015 951793 > 459 [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(4224, 291, F4, 165) (dual of [291, 67, 166]-code) | [i] | Truncation | |
| 2 | No linear OA(4225, 292, F4, 166) (dual of [292, 67, 167]-code) | [i] | ||
| 3 | No linear OA(4226, 293, F4, 167) (dual of [293, 67, 168]-code) | [i] | ||
| 4 | No linear OOA(4224, 290, F4, 2, 165) (dual of [(290, 2), 356, 166]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4225, 290, F4, 2, 166) (dual of [(290, 2), 355, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(4226, 290, F4, 2, 167) (dual of [(290, 2), 354, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(4223, 290, F4, 2, 164) (dual of [(290, 2), 357, 165]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4223, 290, F4, 3, 164) (dual of [(290, 3), 647, 165]-NRT-code) | [i] | ||
| 9 | No digital (59, 223, 290)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |