A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity

The number of $n$-ary balanced correlation immune (resilient) Boolean functions of order $\frac{n}{2}$ is not less than $n^{2^{(n\mathrm{/}2)-2}(1+o(1))}$ as $n\to \mathrm{\infty }$. Keywords: resilient function, correlation immune function, orthogonal array