Summary: We examine the possible orders of t-subset-regular self-complementary \(k\)-uniform hypergraphs, which form examples of large sets of two isomorphic \(t\)-designs. We reformulate Khosrovshahi and Tayfeh -- Rezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank \(k\), and these conditions simplify to a more transparent relation between the order \(n\) and rank \(k\) in the case where \(k\) is a sum of consecutive powers of 2. Moreover, we present new constructions for 1-subset-regular self-complementary uniform hypergraphs, and prove that these necessary conditions are sufficient for all \(k\), in the case where \(t = 1\).