Information on Result #1856439
There is no (100, 109)-sequence in base 2, because net from sequence would yield (100, m, 110)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (100, 871, 110)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2871, 110, S2, 8, 771), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 164625 190444 848374 033579 133993 978438 087949 530281 437216 631177 142690 463495 668819 449971 850765 747400 962317 870658 446689 929498 891587 837339 633494 238803 823919 619767 623714 312428 236660 895199 628262 570937 027271 712259 961630 977206 042016 835925 266340 904732 113311 641645 349704 040448 / 193 > 2871 [i]
- extracting embedded OOA [i] would yield OOA(2871, 110, S2, 8, 771), 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 (100, 109)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (100, m, 109)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (100, 109)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (100, m, 109)-net over F2 with m > ∞ | [i] | ||