Information on Result #1852899
There is no (19, m, 174)-net in base 9 for arbitrarily large m, because m-reduction would yield (19, 345, 174)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9345, 174, S9, 2, 326), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19 136020 092621 986674 220659 413168 430069 475008 425255 137981 694464 368152 546340 183673 886309 531349 165896 101380 895402 249119 551765 847255 762024 027942 836069 129196 522961 741369 664871 345719 553644 091713 590504 032652 614654 081645 262386 095429 668357 613551 982143 255911 602653 476901 337135 687997 951859 010022 240454 339427 013160 244605 035669 240704 033288 205533 / 109 > 9345 [i]
Mode: Bound.
Optimality
Show details for fixed 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 (19, 173)-sequence in base 9 | [i] | Net from Sequence | |
| 2 | No (19, 19+k, 174)-net in base 9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (19, m, 174)-net in base 9 with unbounded m | [i] | ||
| 4 | No digital (19, 19+k, 174)-net over F9 for arbitrarily large k | [i] | ||
| 5 | No digital (19, m, 174)-net over F9 with unbounded m | [i] | ||