Hadamard partitioned difference families and their descendants

If D is a (4u2, 2u2 − u, u2 − u) Hadamard difference set (HDS) in G, then {G,G D} is clearly a (4u2, [2u2 − u, 2u2 + u], 2u2) partitioned difference family (PDF). Any (v,K, λ)-PDF will be said a Hadamard PDF if v = 2λ as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order 4u2(2n + 1) and three block-sizes 4u2 − 2u, 4u2 and 4u2 + 2u, whenever we have a (4u2, 2u2 − u, u2 − u)-HDS and the maximal prime power divisors of 2n + 1 are all greater than 4u2 + 2u.