Information on Result #598860
There is no digital (121, 213, 358)-net over F2, because extracting embedded orthogonal array would yield linear OA(2213, 358, F2, 92) (dual of [358, 145, 93]-code), but
- construction Y1 [i] would yield
- OA(2212, 300, S2, 92), but
- the linear programming bound shows that M ≥ 2484 132694 351399 471861 447697 940992 402712 231248 004226 234322 576635 442083 069406 167011 327832 607273 517056 / 377277 818302 855799 777736 052112 623275 > 2212 [i]
- linear OA(2145, 358, F2, 58) (dual of [358, 213, 59]-code), but
- discarding factors / shortening the dual code would yield linear OA(2145, 343, F2, 58) (dual of [343, 198, 59]-code), but
- the improved Johnson bound shows that N ≤ 7 839683 395577 661521 065550 956096 419139 602118 236678 534951 091663 < 2198 [i]
- discarding factors / shortening the dual code would yield linear OA(2145, 343, F2, 58) (dual of [343, 198, 59]-code), but
- OA(2212, 300, S2, 92), 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 (121, 214, 358)-net over F2 | [i] | m-Reduction | |