  The general solution to the quantum master equation (and its $Sp(2)$
symmetric counterpart) is constructed explicitly in case of finite number of
variables. It is shown that the finite-dimensional solution is physically
trivial and thus can not be extended directly to cover the case of a local
field theory. In this way we conclude that the locality condition plays an
important role by making it possible to obtain nontrivial physical results when
quantizing gauge field theories on the basis of field-antifield formalism.
