In this paper, a relationship is established between orthogonal mappings of a group and difference sets for construction of orthogonal arrays. A difference set D(lO,lO,5) has been constructed and is given as an illustration. Use of difference sets for construction of orthogona:l Latin squares and error correcting codes is discussed.

We present an application of generalized strong complete mappings to construction a family mutually orthogonal Latin squares. also determine cycle structure such mapping which form MOLS. Many constructions over extension finite field are provided.

then it is known, MacNeish [16] and Mann [17] that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v. It seemed plausible that n(v) is also the maximum possible number of m.o.l.s. of order v. This would have implied the correctness of Euler's [13] conjecture about the nonexistence of two orthogonal Latin squares of order v when v = 2 (mod 4), since n(v)...