Nonexistence of binary orthogonal arrays via their distance distributions

We investigate binary orthogonal arrays by making use of the fact that all possible distance distributions of the arrays under investigation and of related arrays can be computed. We apply certain relations for reducing the number of feasible distance distributions. In some cases this leads to nonexistence results. In particular, we prove that there exist no binary orthogonal arrays with parameters $(\text{strength, length, cardinality})=(4,10,6\cdot2^4)$, $(4,11,6\cdot2^4)$, $(4,12,7\cdot2^4)$, $(5,11,6\cdot2^5)$, $(5,12,6\cdot2^5)$ and $(5,13,7\cdot2^5)$.