Simplicity conditions for binary orthogonal arrays

It is known that correlation-immune (CI) Boolean functions used in the framework of side-channel attacks need to have low Hamming weights. The supports CI are (equivalently) simple orthogonal arrays when their elements written as rows an array. minimum weight a function then same number In this paper, we use Rao's Bound give sufficient condition on rows, for binary array (OA) be simple. We apply result determining all strengths 2 and 3; show such case OA, extend observation some OA $4$ $5$. This allows us reply positively, 3, question raised by first author X. Chen monotonicity 2-CI functions, partially positively 4 5.