Complexity of the realization of a linear Boolean function in the class of $\pi$-schemes

Using Khrapchenko's method, we obtain the exact lower bound of 40 for the complexity in the class of $\pi$-schemes of a linear Boolean function depending substantially on 6 variables. We give a simplified proof of several lower bounds for the complexity of linear Boolean functions which are previously obtained on the basis of the same method. Bibliogr. 18.