Information on Result #1850433
There is no (106, m, 226)-net in base 3 for arbitrarily large m, because m-reduction would yield (106, 1123, 226)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31123, 226, S3, 5, 1017), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37525 364226 809373 817770 636870 312419 841614 154099 836924 388847 008161 233264 483972 043007 397848 600873 138244 142646 485057 080004 496493 729743 571398 990705 985510 042630 015217 890476 851808 290851 807458 494080 256764 629699 485476 144976 013206 359276 468900 307670 856170 374982 715744 143559 649064 283591 855829 874015 185250 551826 502902 149249 251109 356672 866983 907282 470149 757118 787135 583904 543640 352205 222449 073953 526982 344003 697134 113391 142970 386318 785262 349008 710409 962907 632221 667788 119432 408851 999187 824003 826330 223750 834930 516315 650190 738834 086400 397844 325785 503795 / 509 > 31123 [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 (106, 225)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (106, 106+k, 226)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (106, m, 226)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (106, 106+k, 226)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (106, m, 226)-net over F3 with unbounded m | [i] | ||