A patterned magnetic medium is the next step to significantly increasing data storage density. To attain extreme density, it is necessary to deal with the smallest granules (each storing a bit of information) admissible from the physical point of view. It is well known that the volume of such granules, and their aspect ratio, have to be large enough to prevent thermally activated magnetization relaxation. However, these requirements are not exhaustive. A patterned recording medium is a set of closely-spaced, aligned magnetic granules, with the random (“up” and “down”) orientations of granules' magnetic moments. Though the exchange interactions between the granules may be neglected, there are long-range intergranular dipole-dipole interactions (DDI) which lead to significant lowering of activation barrier preventing thermal relaxation. Those interactions limit the acceptable density of ferromagnetic granules, and hence, reduce the extreme density of data storage. Our numerical calculations estimate the negative role of DDI for the particular case of a two-dimensional set of ellipsoidal magnetic granules and allow us to determine the extreme density of data storage.