Information on Result #1852908
There is no (22, m, 199)-net in base 9 for arbitrarily large m, because m-reduction would yield (22, 395, 199)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9395, 199, S9, 2, 373), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17 448639 662793 068196 353249 913700 521054 024981 923750 530348 209777 366334 225490 918082 529810 808663 906780 554393 741139 229391 884531 720284 969371 758690 010046 234413 764814 257207 386607 372594 438105 884569 687286 523034 706926 571643 372425 314231 066152 217354 760108 275335 488172 034670 736226 618611 381117 942108 463114 298187 740523 963340 142190 045922 864831 985299 089009 840902 169619 460049 913319 930931 430459 301943 / 187 > 9395 [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 (22, 198)-sequence in base 9 | [i] | Net from Sequence | |
| 2 | No (22, 22+k, 199)-net in base 9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (22, m, 199)-net in base 9 with unbounded m | [i] | ||
| 4 | No digital (22, 22+k, 199)-net over F9 for arbitrarily large k | [i] | ||
| 5 | No digital (22, m, 199)-net over F9 with unbounded m | [i] | ||