  We develop and apply combinatorial algorithms for investigation of the
feasible distance distributions of binary orthogonal arrays with respect to a
point of the ambient binary Hamming space utilizing constraints imposed from
the relations between the distance distributions of connected arrays. This
turns out to be strong enough and we prove the nonexistence of binary
orthogonal arrays of parameters (length, cardinality, strength)$\
=(9,6.2^4=96,4)$, $(10,6.2^5,5)$, $(10,7.2^4=112,4)$, $(11,7.2^5,5)$,
$(11,7.2^4,4)$ and $(12,7.2^5,5)$, resolving the first cases where the
existence was undecided so far. For the existing arrays our approach allows
substantial reduction of the number of feasible distance distributions which
could be helpful for classification results (uniqueness, for example).
