Room squares with holes of sides 3, 5, and 7

We investigate Room squares and subsquares. All terminology is as in [6] and [7], and we will assume the reader is familiar with the definitions contained therein. (These include group-divisible designs, transverial designs, and frames.) We will refer to an incomplete Room square of side s missing a subsquare of side t as an (s, t)-incompZefe Room square. It is known that for any odd t, there is a constant S(t) such that there exists an (s, t)-incomplete Room square for all odd s > S(t). The following was proved in [7].