Collective rearrangement is an important class of algorithms for the computer generation of random sphere packings, especially for those of low porosity. In this paper we examine how the choice of boundary conditions affects internal packing structure. The results help to quantify the depth to which non-periodic boundaries influence internal structure. Mon interesting results are obtained for periodic boundary conditions, showing that for small packings, self-assembly into ordered packings is possible, even without a seed structure or undue influence from the algorithm. Furthermore, the structure depends on the shape of the periodic domain. Finally, we propose examining the transition from random to ordered packings to better characterize the random-close-packed (RCP) limit and its associated packing structures.