The Latin squares of order k are widely used to make a three-factor experiment , when each factor has k levels . In some experiments , the size of the blocks may be less than the numbers of treatments . In order to compare all treatments in each block , a new class of Latin squares , called quot; incomplete Latin squares, quot; is introduced . One of the most important types of incomplete Latin squares is the balanced incomplete Latin square with parameters k and r , which is denoted by BILS‌(k,r) . It is obtained from an incomplete Latin square such that each of the k labels occurs exactly r times in the square . A transversal in a Latin square of order k is a set of k entries , one selected from each row and each column of the Latin square such that no two entries contain the same symbol .