$k$-seminets [1] are a generalization of $k$-nets [5,6]. In [2] reconsidered a class of finite $k$-seminets, and a connection of a subclass of it with Sperner affine spaces is established [3,4]. In this paper we describe a construction of such $k$-seminets, using $\bar{k}$-nets which are in bijection with affine planes.