Information on Result #598864
There is no digital (122, 216, 353)-net over F2, because extracting embedded orthogonal array would yield linear OA(2216, 353, F2, 94) (dual of [353, 137, 95]-code), but
- construction Y1 [i] would yield
- OA(2215, 299, S2, 94), but
- adding a parity check bit [i] would yield OA(2216, 300, S2, 95), but
- the linear programming bound shows that M ≥ 872407 680551 113098 866799 953294 886066 311827 924058 628412 428016 149220 115296 187426 023936 653562 740736 / 5 938078 052347 021578 779474 608305 > 2216 [i]
- adding a parity check bit [i] would yield OA(2216, 300, S2, 95), but
- linear OA(2137, 353, F2, 54) (dual of [353, 216, 55]-code), but
- discarding factors / shortening the dual code would yield linear OA(2137, 349, F2, 54) (dual of [349, 212, 55]-code), but
- the improved Johnson bound shows that N ≤ 38183 360155 231925 981960 410163 248656 002020 375812 982277 632854 212429 < 2212 [i]
- discarding factors / shortening the dual code would yield linear OA(2137, 349, F2, 54) (dual of [349, 212, 55]-code), but
- OA(2215, 299, S2, 94), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (122, 217, 353)-net over F2 | [i] | m-Reduction | |