Classification of semiregular relative difference sets withgcd(,n)=1 attaining Turyn's bound

Suppose a(lambda n,n,lambda n,lambda)relative difference set exists in an abelian groupG=SxH,where|S|=lambda,|H|=n(2),gcd(lambda,n)=1, and lambda is self-conjugate modulo lambda n.Then lambda is a square,say lambda=u(2),andexp(S)dividesuby Turyn's exponent bound. We classify all such relativedifference sets with exp(S)=u. We also show thatnmust be a prime power if an abelian(lambda n,n,lambda n,lambda)RDS with gcd(lambda,n)=1 exists and lambda is self-conjugate modulon