A series of Siamese twin designs

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