  A Boolean function $f$ on $n$ variables is said to be a bent function if the
absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a
new asymptotic lower bound on the number of Boolean bent functions. It is based
on a modification of the Maiorana--McFarland family of bent functions and
recent progress in the estimation of the number of transversals in latin
squares and hypercubes. By-products of our proofs are the asymptotics of the
logarithm of the numbers of partitions of the Boolean hypercube into
$2$-dimensional affine and linear subspaces.
