Information on Result #1856445
There is no (106, 116)-sequence in base 2, because net from sequence would yield (106, m, 117)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (106, 693, 117)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2693, 117, S2, 6, 587), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 054740 586542 333401 266011 673000 050259 980601 485477 802288 866515 977761 223497 772297 196138 150990 733432 988760 540222 209444 616294 148215 722728 048384 034302 644785 890957 013759 246534 548671 168618 655423 563561 434098 926459 289600 / 49 > 2693 [i]
- extracting embedded OOA [i] would yield OOA(2693, 117, S2, 6, 587), 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 (106, 116)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (106, m, 116)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (106, 116)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (106, m, 116)-net over F2 with m > ∞ | [i] | ||