Information on Result #1856385
There is no (46, 54)-sequence in base 2, because net from sequence would yield (46, m, 55)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (46, 322, 55)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2322, 55, S2, 6, 276), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2494 832857 955622 976237 385352 806036 869855 958882 112570 435298 144597 936352 639711 788162 426819 717541 920768 / 277 > 2322 [i]
- extracting embedded OOA [i] would yield OOA(2322, 55, S2, 6, 276), 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 (46, 54)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (46, m, 54)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (46, 54)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (46, m, 54)-net over F2 with m > ∞ | [i] | ||