Information on Result #1856461
There is no (122, 132)-sequence in base 2, because net from sequence would yield (122, m, 133)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (122, 921, 133)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2921, 133, S2, 7, 799), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 545 093654 819629 540217 404625 631683 376121 953144 085721 726607 858951 973499 956222 563201 028274 603733 501527 078584 560829 978393 570202 332690 960238 582069 492821 322663 244519 547859 951965 703055 114830 761011 307343 958083 037225 087810 594836 148458 657416 234383 492657 199335 725550 496491 371695 033678 823424 / 25 > 2921 [i]
- extracting embedded OOA [i] would yield OOA(2921, 133, S2, 7, 799), 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 (122, 132)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (122, m, 132)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (122, 132)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (122, m, 132)-net over F2 with m > ∞ | [i] | ||