Let and be integers. A SOMA, or more specifically a SOMA, is an array , whose entries are -subsets of a -set , such that each element of occurs exactly once in each row and exactly once in each column of , and no 2-subset of is contained in more than one entry of (Soicher 1999).
A SOMA can be constructed by superposing mutually orthogonal Latin squares of order with pairwise disjoint symbol-sets, and so a SOMA can be seen as a generalization of mutually orthogonal Latin squares of order .