Existence of Latin Maps

Abstract

The Latin square (or Latin cube) plays an important role in comparative experiment design. It is generally restricted to 2 or 3 dimensions [1]. For higher dimensions, a new definition - the Latin map - is used [5]. In this paper, the Latin map is studied in 3 aspects. Firstly, the distribution lemma is proved, which gives two conditions for a map to be a Latin map. Secondly, the distribution lemma is used to prove the existence and non-existence of two classes of Latin maps. Finally, an algorithm of finding a Latin map is introduced.