Information on Result #1856452
There is no (113, 123)-sequence in base 2, because net from sequence would yield (113, m, 124)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (113, 858, 124)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2858, 124, S2, 7, 745), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1014 776034 715873 720684 741443 386595 231429 787920 740899 294045 678304 850603 383056 116311 499835 541721 706232 086537 349665 158267 971309 685931 982741 617205 773147 828702 700672 249808 672767 119573 437380 797816 007092 467025 269927 062172 028523 267991 930326 776759 329910 401937 327974 776832 / 373 > 2858 [i]
- extracting embedded OOA [i] would yield OOA(2858, 124, S2, 7, 745), 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 (113, 123)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (113, m, 123)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (113, 123)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (113, m, 123)-net over F2 with m > ∞ | [i] | ||