Mathematical and computational techniques are described for constructing and enumerating generalized Bhaskar Rao designs (GBRD's). In particular, these methods are applied to GBRD(k + l,k,l(k -1); G)'s for / > 1. Properties of the enumerated designs, such as automorphism groups, resolutions and contracted designs, are tabulated. Also described are applications to group divisible designs, multi-dimensional Howell cubes, generalized Room squares, equidistant permutation arrays, and doubly resolvable two-fold triple systems.
Two Steiner triple systems (V, ๐) and (V, ๐) are orthogonal if they have no triples in common, and if for every two distinct intersecting triples {x,y,z} and {x, y, z} of ๐, the two triples {x,y,a} and {u, v, b} in (๐ satisfy a โ b. It is shown here that if v โก 1,3 (mod 6), v โฅ 7 and v โ 9, a pair of orthogonal Steiner triple systems of order v exist. This settles completely the question of their existence posed by O'Shaughnessy in 1968.
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