Estimates of the capacity of orthogonal arrays of large strength

D. G. Fon-Der-Flaass showed that Boolean correlation-immune $n$-variable functions of order $m$ are resilient for $m\ge\frac{2n-2}{3}$. In this paper this theorem is generalized to orthogonal arrays. It is shown that orthogonal arrays of strength $m$ not less than $\frac{2n-2}{3}$, where $n$ is a number of factors having size at least $2^{n-1}$ and all arrays of size $2^{n-1}$ are simple.