Information on Result #1856499
There is no (160, 170)-sequence in base 2, because net from sequence would yield (160, m, 171)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (160, 1358, 171)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21358, 171, S2, 8, 1198), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 780 109913 453544 981658 751755 997510 743349 992538 694382 721233 683472 008108 825456 381769 819619 605070 474063 233733 726062 515395 924405 722240 919509 952946 532881 128435 278652 935529 933660 249720 114323 107099 687236 618018 642009 291247 960578 081761 307667 703566 004112 079165 132627 802703 263577 320300 646873 616405 965793 544261 934428 661758 047749 375500 478712 101860 012423 326097 034602 659371 023050 193233 490947 834587 013028 759547 090141 812155 744256 / 109 > 21358 [i]
- extracting embedded OOA [i] would yield OOA(21358, 171, S2, 8, 1198), 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 (160, 170)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (160, m, 170)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (160, 170)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (160, m, 170)-net over F2 with m > ∞ | [i] | ||