Approximate counting of regular hypergraphs

<p>In this paper we asymptotically count <em>d</em>-regular <em>k</em>-uniform hypergraphs on <em>n</em> vertices, provided <em>k </em> is fixed and d=d(n)=o(n<sup>1/2</sup>). In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.</p>