Packing Costas Arrays

Abstract

A Costas Latin square of order $n$ is a set of $n$ disjoint Costas arrays of the same order. Costas Latin squares are studied here from both a construction and classification point of view. A complete classification is carried out up to order $27$. In this range, we verify the conjecture that there is no Costas Latin square for any odd order $n\ge 3$. Various other related combinatorial structures are also considered, including near Costas Latin squares (which are certain packings of near Costas arrays) and Vatican Costas squares.