Information on Result #599245
There is no digital (78, 222, 273)-net over F3, because extracting embedded orthogonal array would yield linear OA(3222, 273, F3, 144) (dual of [273, 51, 145]-code), but
- residual code [i] would yield OA(378, 128, S3, 48), but
- the linear programming bound shows that M ≥ 6 575490 843517 549614 037804 755790 886921 388297 503372 467014 072409 123799 884455 544386 348644 065807 588730 807152 499714 277823 942029 / 372064 864657 803488 591486 645857 495615 261692 996975 549874 881531 815830 072025 751212 712500 > 378 [i]
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, 223, 273)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (78, 224, 273)-net over F3 | [i] | ||