Complementary partial resolution squares for Steiner triple systems

In this paper, we introduce a generalization of frames called partial resolution squares. We are interested in constructing sets of complementary partial resolution squares for Steiner triple systems. Our main result is the existence of six complementary partial resolution squares for Steiner triple systems of order v which can be superimposed in a v × v array so that the resulting array is also the array formed by the superposition of three mutually orthogonal Latin squares of order v where v ≡ 1 (mod 6), v ≥ 7, and v / ∈ {55, 115, 145, 205, 235, 265, 319, 355, 415, 493, 649, 697}.