Information on Result #551580
There is no linear OOA(2121, 162, F2, 2, 57) (dual of [(162, 2), 203, 58]-NRT-code), because 1 step m-reduction would yield linear OA(2120, 162, F2, 56) (dual of [162, 42, 57]-code), but
- construction Y1 [i] would yield
- OA(2119, 146, S2, 56), but
- the linear programming bound shows that M ≥ 5165 551323 791927 774620 548045 364260 917630 468096 / 7704 797749 > 2119 [i]
- OA(242, 162, S2, 16), but
- discarding factors would yield OA(242, 146, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 467697 956730 > 242 [i]
- discarding factors would yield OA(242, 146, S2, 16), but
- OA(2119, 146, S2, 56), 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(2121, 162, F2, 3, 57) (dual of [(162, 3), 365, 58]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2121, 162, F2, 4, 57) (dual of [(162, 4), 527, 58]-NRT-code) | [i] | ||
| 3 | No linear OOA(2121, 162, F2, 5, 57) (dual of [(162, 5), 689, 58]-NRT-code) | [i] | ||
| 4 | No linear OOA(2121, 162, F2, 6, 57) (dual of [(162, 6), 851, 58]-NRT-code) | [i] | ||
| 5 | No linear OOA(2121, 162, F2, 7, 57) (dual of [(162, 7), 1013, 58]-NRT-code) | [i] | ||
| 6 | No linear OOA(2121, 162, F2, 8, 57) (dual of [(162, 8), 1175, 58]-NRT-code) | [i] | ||