Information on Result #547876
There is no linear OA(4140, 204, F4, 102) (dual of [204, 64, 103]-code), because construction Y1 would yield
- linear OA(4139, 163, F4, 102) (dual of [163, 24, 103]-code), but
- construction Y1 [i] would yield
- OA(4138, 149, S4, 102), but
- the linear programming bound shows that M ≥ 11 769278 720446 703333 267659 747956 551886 187319 922656 933070 157940 129170 842786 675855 465333 653504 / 85 907459 > 4138 [i]
- OA(424, 163, S4, 14), but
- discarding factors would yield OA(424, 134, S4, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 292 368491 029312 > 424 [i]
- discarding factors would yield OA(424, 134, S4, 14), but
- OA(4138, 149, S4, 102), but
- construction Y1 [i] would yield
- OA(464, 204, S4, 41), but
- discarding factors would yield OA(464, 203, S4, 41), but
- the linear programming bound shows that M ≥ 9237 828678 014661 888733 201438 074087 629177 850315 553208 766694 988543 356653 154675 278877 490717 655040 / 25 848321 162508 053807 967718 560003 483887 415061 992757 599441 > 464 [i]
- discarding factors would yield OA(464, 203, S4, 41), but
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(4141, 205, F4, 103) (dual of [205, 64, 104]-code) | [i] | Truncation | |
| 2 | No linear OOA(4141, 204, F4, 2, 103) (dual of [(204, 2), 267, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(4140, 204, F4, 2, 102) (dual of [(204, 2), 268, 103]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(4140, 204, F4, 3, 102) (dual of [(204, 3), 472, 103]-NRT-code) | [i] | ||
| 5 | No digital (38, 140, 204)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |