  We introduce a parameter space containing all algebraic integers
$\beta\in(1,2]$ that are not Pisot or Salem numbers, and a sequence of
increasing piecewise continuous function on this parameter space which gives a
lower bound for the Garsia entropy of the Bernoulli convolution $\nu_{\beta}$.
This allows us to show that $\mathrm{dim}_\mathrm{H} (\nu_{\beta})=1$ for all
$\beta$ with representations in certain open regions of the parameter space.
