Information on Result #1856390
There is no (51, 59)-sequence in base 2, because net from sequence would yield (51, m, 60)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (51, 412, 60)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2412, 60, S2, 7, 361), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 073071 518126 219606 313206 405990 769980 901877 085775 985903 676658 621980 536561 317072 380507 793363 938947 133282 046040 910473 251642 146816 / 181 > 2412 [i]
- extracting embedded OOA [i] would yield OOA(2412, 60, S2, 7, 361), 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 (51, 59)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (51, m, 59)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (51, 59)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (51, m, 59)-net over F2 with m > ∞ | [i] | ||