Information on Result #1856449
There is no (110, 120)-sequence in base 2, because net from sequence would yield (110, m, 121)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (110, 837, 121)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2837, 121, S2, 7, 727), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 123 720064 927811 832403 089146 593475 302279 917913 223777 218927 187062 713983 796503 124545 968371 628028 362394 581854 833079 826078 790721 394438 470556 987345 922512 499558 983960 615617 010470 196281 792581 449589 188313 378572 835561 139469 096019 991581 106361 218349 960299 968955 678720 / 91 > 2837 [i]
- extracting embedded OOA [i] would yield OOA(2837, 121, S2, 7, 727), 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 (110, 120)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (110, m, 120)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (110, 120)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (110, m, 120)-net over F2 with m > ∞ | [i] | ||