A lower bound on the number of bent squares

Bent functions are Boolean functions that are maximally nonlinear. They can be represented as bent squares, i.e., square matrices for which each row and each column is the Walsh spectrum of a Boolean function. Using this representation, it is shown in this note that the number of bent functions in $n$ variables is at least $2^{n \cdot 2^{\frac{n}{2}} \left(1 + O\left(\frac{1}{n}\right)\right)}$ for even integers $n$.