Complete sets of pairwise orthogonal Latin squares and the corresponding projective planes

AbstractWe define several types of transformations on the class of complete sets of pairwise orthogonal Latin squares (POLS) of order n and describe their geometrical effects in the corresponding projective planes. We establish a set of necessary and sufficient conditions that a projective plane of order n should be (V, l)-transitive (in the case where V lies on l) in terms of the properties of a corresponding complete set of POLS. We apply these ideas to determine which plane is represented by a particular complete set of POLS of order nine due to Paige and Wexler and find an answer different from that which has been given in the literature