  We have determined the maximum quantum violation of 241 tight bipartite Bell
inequalities with up to five two-outcome measurement settings per party by
constructing the appropriate measurement operators in up to six-dimensional
complex and eight-dimensional real component Hilbert spaces using numerical
optimization. Out of these inequalities 129 has been introduced here. In 43
cases higher dimensional component spaces gave larger violation than qubits,
and in 3 occasions the maximum was achieved with six-dimensional spaces. We
have also calculated upper bounds on these Bell inequalities using a method
proposed recently. For all but 20 inequalities the best solution found matched
the upper bound. Surprisingly, the simplest inequality of the set examined,
with only three measurement settings per party, was not among them, despite the
high dimensionality of the Hilbert space considered. We also computed detection
threshold efficiencies for the maximally entangled qubit pair. These could be
lowered in several instances if degenerate measurements were also allowed.
