On the maximum number of different ordered pairs of symbols in sets of latin squares

In this paper, we study the problem of constructing sets of s latin squares of order m such that the average number of different ordered pairs obtained by superimposing two of the s squares in the set is as large as possible. We solve this problem (for all s) when m is a prime power by using projective planes. We also present upper and lower bounds for all positive integers m. © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 1–15, 2005.