Information on Result #1857282
There is no (19, 133)-sequence in base 7, because net from sequence would yield (19, m, 134)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (19, 265, 134)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7265, 134, S7, 2, 246), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26887 294207 970268 759601 657658 889776 095045 375361 275265 172861 260229 563982 961931 156601 013406 360427 771092 477311 182639 767908 335162 075873 790268 224023 707340 408699 369167 136353 848535 631815 185217 453099 342933 554750 719155 927758 584420 150907 / 247 > 7265 [i]
- extracting embedded OOA [i] would yield OOA(7265, 134, S7, 2, 246), but
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, 133)-sequence in base 7 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (19, m, 133)-net in base 7 with m > ∞ | [i] | ||
| 3 | No digital (19, 133)-sequence over F7 (for arbitrarily large k) | [i] | ||
| 4 | No digital (19, m, 133)-net over F7 with m > ∞ | [i] | ||