Designs With Mutually Orthogonal Resolutions

Mutually Orthogonal Latin Squares and Self-complementary Designs

Suppose that n is even and a set of n 2 − 1 mutually orthogonal Latin squares of order n exists. Then we can construct a strongly regular graph with parameters (n, n 2 (n−1), n 2 ( 2 −1), n 2 ( 2 −1)), which is called a Latin square graph. In this paper, we give a sufficient condition of the Latin square graph for the existence of a projective plane of order n. For the existence of a Latin squa...

More mutually orthogonal Latin squares

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares. As an application of such constructions we obtain some new infinite classes of pairwise orthogonal diagonal Latin squares which are useful in the study of pairwise orthogonal diagonal Latin squares.

Orthogonal resolutions of triple systems

Existence results concerning double and multiple orthogonal resolutions of triple are and a number of open nlll~~tl0Tl!'l mentioned.

New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

Using Hadamard matrices and mutually orthogonal Latin squares, we construct two new quasi-symmetric designs, with parameters 2 − (66, 30, 29) and 2− (78, 36, 30). These are the first examples of quasisymmetric designs with these parameters. The parameters belong to the families 2− (2u2−u, u2−u, u2−u−1) and 2− (2u2 +u, u2, u2−u) which are related to Hadamard parameters. The designs correspond to...

Generalized orthogonal designs