Information on Result #547359
There is no linear OA(4222, 275, F4, 164) (dual of [275, 53, 165]-code), because residual code would yield OA(458, 110, S4, 41), but
- the linear programming bound shows that M ≥ 1232 155961 216230 168086 977678 056475 191089 409710 805770 829825 897828 417067 677196 009558 961106 027628 461497 995772 222254 044023 160230 949557 990006 504845 840607 997118 369373 847851 273455 403008 / 13446 810158 281327 760184 995983 919490 800441 646762 168115 151101 794360 608708 987818 154852 821096 884734 101312 394526 499211 581201 357552 019470 400051 102575 > 458 [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(4223, 276, F4, 165) (dual of [276, 53, 166]-code) | [i] | Truncation | |
| 2 | No linear OA(4224, 277, F4, 166) (dual of [277, 53, 167]-code) | [i] | ||
| 3 | No linear OA(4225, 278, F4, 167) (dual of [278, 53, 168]-code) | [i] | ||
| 4 | No linear OOA(4223, 275, F4, 2, 165) (dual of [(275, 2), 327, 166]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4224, 275, F4, 2, 166) (dual of [(275, 2), 326, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(4225, 275, F4, 2, 167) (dual of [(275, 2), 325, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(4222, 275, F4, 2, 164) (dual of [(275, 2), 328, 165]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4222, 275, F4, 3, 164) (dual of [(275, 3), 603, 165]-NRT-code) | [i] | ||
| 9 | No digital (58, 222, 275)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |