Abstract
In this paper we develop a theory of t t -cycle D − Z D-Z representations for s s -dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a D D -matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their Z Z -matrix is a column permuted version of a unit upper triangular matrix. Triangular forms may be obtained constructively using sequences of elementary transformations based on elementary matrix algebra. Our main result is to define a unique canonical form for prime-power rules. This ultratriangular form is a triangular form, is easy to recognize, and may be derived in a straightforward manner.
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