NEW CONSTRUCTIONS OF DIVISIBLE DESIGNS

A construction is given for a (p2a(p+1),p2,p2a+1(p+1),p2a+1,p2a(p+1)) (p a prime) divisible difference set in the group H X Z(pa+1)2 where H is any abelian group of order p+1. This can be used to generate a sym metric semi-regular divisible design; this is a new set of parameters for lambda1 not-equal 0, and those are fairly rare. We also give a con struction for a (p(a-1)+P(a-2)+...+p+2,p(a+2), .+p+1),p(a)(p(a-1)+...p+1),p(a-1)(p(a)+...+p2+2)) divisible difference set in the group H x Z(p2) x Z(p)a. This is another new set of parameters, and it correspon ds to a symmetric regular divisible design. For p = 2, these parameter s have lambda1 = lambda2, and this corresponds to the parameters for t he ordinary Menon difference sets.