Information on Result #551846
There is no linear OOA(2136, 158, F2, 2, 67) (dual of [(158, 2), 180, 68]-NRT-code), because 1 step m-reduction would yield linear OA(2135, 158, F2, 66) (dual of [158, 23, 67]-code), but
- construction Y1 [i] would yield
- OA(2134, 150, S2, 66), but
- the linear programming bound shows that M ≥ 235 377396 587616 186439 177776 455843 253082 652672 / 10387 > 2134 [i]
- OA(223, 158, S2, 8), but
- discarding factors would yield OA(223, 120, S2, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 8 502671 > 223 [i]
- discarding factors would yield OA(223, 120, S2, 8), but
- OA(2134, 150, S2, 66), 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(2136, 158, F2, 3, 67) (dual of [(158, 3), 338, 68]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(2136, 158, F2, 4, 67) (dual of [(158, 4), 496, 68]-NRT-code) | [i] | ||
| 3 | No linear OOA(2136, 158, F2, 5, 67) (dual of [(158, 5), 654, 68]-NRT-code) | [i] | ||
| 4 | No linear OOA(2136, 158, F2, 6, 67) (dual of [(158, 6), 812, 68]-NRT-code) | [i] | ||
| 5 | No linear OOA(2136, 158, F2, 7, 67) (dual of [(158, 7), 970, 68]-NRT-code) | [i] | ||
| 6 | No linear OOA(2136, 158, F2, 8, 67) (dual of [(158, 8), 1128, 68]-NRT-code) | [i] | ||