Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

AbstractUsing affine resolvable designs and complete sets of mutually orthogonal frequency squares and hypercubes, we provide several generalizations of Bose's equivalence between affine planes of order n and complete sets of mutually orthogonal latin squares of order n. We also characterize those complete sets of orthogonal frequency squares and hypercubes which are equivalent to affine geometries