Abstract: A Latin square arrangement is an arrangement of s symbols in s rows and s columns, such that every symbol occurs once in each row and each column. When two Latin squares of same order superimposed on one another, then in the resultant array every ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal. A frequency square M of type F (n; λ) is ...

A latin square of order n possessing a cyclic automorphism of order n is said to be diagonally cyclic because its entries occur in cyclic order down each broken diagonal. More generally, we consider squares possessing any cyclic automorphism. Such squares will be named after Parker, in recognition of his seminal contribution to the study of orthogonal latin squares. Our primary aim is to survey...

We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k, s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bound...