A New Family of Symmetric 2-(v, k, λ) Block Designs

We utilize cyclic relative difference sets (m, n, k, λ), with parameters m = (qr - 1)/(q - 1), n = q - 1, k = qr - 1, λ = qr - 2, where q is an odd prime power, to construct a new family of 2-(v, k, λ) designs with v = (q + 1)(q2t - 1)/(q - 1), k = q2t - 1(q + 1)/2, λ = q2t - 2(q2 - 1)/4, (t ⩾ 2), when q is of the form 2p - 1.