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 
.
