Information on Result #559853
There is no linear OOA(4144, 163, F4, 2, 107) (dual of [(163, 2), 182, 108]-NRT-code), because 5 step m-reduction 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
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 OOA(4144, 163, F4, 3, 107) (dual of [(163, 3), 345, 108]-NRT-code) | [i] | Depth Reduction | |