A series of Siamese twin designs

A {0,±1}{0,±1}-matrix SS is called a Siamese twin design sharing the entries of II if S=I+K−LS=I+K−L, where I,K,LI,K,L are nonzero {0,1}{0,1}-matrices and both I+KI+K and I+LI+L are incidence matrices of symmetric designs with the same parameters. Let pp and 2p+32p+3 be prime powers and p≡3(mod4). We construct a Siamese twin design with parameters (4(p+1)2,2p2+3p+1,p2+p)(4(p+1)2,2p2+3p+1,p2+p).