Information on Result #1856446
There is no (107, 117)-sequence in base 2, because net from sequence would yield (107, m, 118)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (107, 816, 118)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2816, 118, S2, 7, 709), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 241 221236 618014 199597 765636 160103 009748 510742 539035 037174 250491 877375 905318 524217 162454 176555 407636 462967 017350 599484 946915 696214 872810 423868 494482 039545 409401 292520 416328 812873 096836 797125 187446 399873 116209 768319 804590 844587 999666 682099 158977 871872 / 355 > 2816 [i]
- extracting embedded OOA [i] would yield OOA(2816, 118, S2, 7, 709), 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 (107, 117)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (107, m, 117)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (107, 117)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (107, m, 117)-net over F2 with m > ∞ | [i] | ||