In this letter, we study an abstract model of neocortex based on its modularization into mini- and hypercolumns. We discuss a full-scale instance of this model and connect its network properties to the underlying biological properties of neurons in cortex. In particular, we discuss how the biological constraints put on the network determine the network's performance in terms of storage capacity. We show that a network instantiating the model scales well given the biologically constrained parameters on activity and connectivity, which makes this network interesting also as an engineered system. In this model, the minicolumns are grouped into hypercolumns that can be active or quiescent, and the model predicts that only a few percent of the hypercolumns should be active at any one time. With this model, we show that at least 20 to 30 pyramidal neurons should be aggregated into a minicolumn and at least 50 to 60 minicolumns should be grouped into a hypercolumn in order to achieve high storage capacity.