Relative difference sets in Alt(5)

This paper is motivated by Itoʹs paper ((Hokkaido) Math. J. 22 (1993) 373), in which he constructed ( 60 , 2 , 60 , 30 ) -relative difference sets in SL ( 2 , 5 ) . Chen and Li have shown that Alt ( 5 ) , the alternating group of degree 5, has a (30,2,29,14)-relative difference set (see Discrete Math. 256 (2002) 301). These are the only examples of nontrivial relative difference sets in nonsolvable groups known to the author. In this paper, we study relative difference sets in Alt ( 5 ) and show that there exist exactly two nontrivial relative difference sets in Alt ( 5 ) up to equivalence with the aid of a computer.