Information on Result #599243
There is no digital (78, 216, 334)-net over F3, because extracting embedded orthogonal array would yield linear OA(3216, 334, F3, 138) (dual of [334, 118, 139]-code), but
- residual code [i] would yield OA(378, 195, S3, 46), but
- 4 times truncation [i] would yield OA(374, 191, S3, 42), but
- the linear programming bound shows that M ≥ 7425 373872 326041 246958 413277 162396 664697 868093 270451 580073 051722 485491 109207 030427 537458 984375 / 32911 891840 780579 755648 777011 603243 208306 897748 202179 983781 > 374 [i]
- 4 times truncation [i] would yield OA(374, 191, S3, 42), 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 (78, 217, 334)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (78, 218, 334)-net over F3 | [i] | ||