Information on Result #1849551
There is no (46, m, 55)-net in base 2 for arbitrarily large m, because m-reduction 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]
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 | [i] | Net from Sequence | |
| 2 | No (46, 46+k, 55)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (46, m, 55)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (46, 46+k, 55)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (46, m, 55)-net over F2 with unbounded m | [i] | ||