On Multiplexer Function Complexity in the $\pi$-schemes Class

It is proven that $n$-th's order multiplexer realization complexity in $\pi$-schemes class is equal to $2^{n+1}+\frac{2^n}n\pm O(\frac{2^n}{n\log n})$ and, thus, the so-called high-accuracy asymptotic bounds for the stated complexity are established for the first time.