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A hypergraph \( H \) with vertex set \( V \) and edge set \( E \) is called bipartite if \( V \) can be partitioned into two subsets \( V_1 \) and \( V_2 \) such that \( e \cap V_1 \neq \phi \) and \( e \cap V_2 \neq \phi \) for any \( e \in E \). A bipartite self-complementary 3-uniform hypergraph \( H \) with partition \( (V_1, V_2) \) of a vertex set \( V \) such that \( |V_1| = m \) and \( |V_2| = n \) exists if and only if either (i) \( m = n \) or (ii) \( m \neq n \) and either \( m \) or \( n \) is congruent to 0 modulo 4 or (iii) \( m \neq n \) and both \( m \) and \( n \) are congruent to 1 or 2 modulo 4.
In this paper we prove that, there exists a regular bipartite self-complementary 3-uniform hypergraph \( H(V_1, V_2) \) with \( |V_1| = m, |V_2| = n, m + n > 3 \) if and only if \( m = n \) and \( n \) is congruent to 0 or 1 modulo 4. Further we prove that, there exists a quasi-regular bipartite self-complementary 3-uniform hypergraph \( H(V_1, V_2) \) with \( |V_1| = m, |V_2| = n, m + n > 3 \) if and only if either \( m = 3, n = 4 \) or \( m = n \) and \( n \) is congruent to 2 or 3 modulo 4.