Information on Result #1856503
There is no (164, 174)-sequence in base 2, because net from sequence would yield (164, m, 175)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (164, 1390, 175)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21390, 175, S2, 8, 1226), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 36 423683 632146 431599 092908 269440 765436 536913 734702 027937 621752 624036 075263 631370 189251 511281 617647 499462 136595 077897 507943 271206 213647 619641 189548 324802 937995 044538 611307 272259 854173 086113 528333 076635 879059 972776 904829 423264 105828 458082 158879 047399 243747 351980 833514 936411 869244 700378 570642 324037 990958 429198 725972 245228 977940 618609 964989 717752 973594 810251 387707 762141 585716 968850 223271 502381 634237 960093 875472 078263 549952 / 1227 > 21390 [i]
- extracting embedded OOA [i] would yield OOA(21390, 175, S2, 8, 1226), 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 (164, 174)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (164, m, 174)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (164, 174)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (164, m, 174)-net over F2 with m > ∞ | [i] | ||