A computer-implemented database and method providing an efficient, ordered reduced space representation of multi-dimensional data. The data values for each attribute are stored in a manner that provides an advantage in, for example, space usage and/or speed of access, such as in condensed form and/or sort order. Instances of each data value for an attribute are identified by instance elements, each of which is associated with one data value. Connectivity information is provided for each instance element that uniquely associates each instance element with a specific instance of a data value for another attribute. Low cardinality fields may be combined into a single field having values representing the various combinations of the original fields. In one embodiment, the “combined field” contains only instantiated combinations. In another embodiment, the combined field contains all values in the Cartesian product of the original fields, preferably in nested sort order. In yet another embodiment, the original fields are padded with dummy values so that their cardinalities are a power of two, causing each subfield in the combined field to fall on a bit boundary. In still another embodiment, containerization techniques are used to reduce the space required for representing the complete set of all possible values in the Cartesian product of the original fields.
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