A system provides multidimensional tuple Hilbert ordering within a linear storage structure to enable more consistent and efficient access to stored multidimensional tuples. The database system comprises a tuple storage module that receives multidimensional data elements, where each multidimensional data element is defined by a plurality of different object types, and where each object is associated with a different dimension within a multidimensional data space. The tuple storage module further forms a respective tuple for each of the multidimensional data elements by mapping each object to an associated reference and applies a Hilbert function to the references of each of the tuples to determine a respective Hilbert ordering for each of the tuples. The system further comprises a linear data storage structure that includes a B-tree for storing the Hilbert ordering.