Lattice rules are equal weight numerical quadrature rules for the integration of periodic functions over the s-dimensional unit hypercube U s = [0, 1) s . For a given lattice rule, say Q L , a set of points L (the integration lattice), regularly spaced in all of R s , is generated by a finite number of rational vectors. The abscissa set forQ L is thenP (Q L ) = L [cap ] U s . It is known thatP (Q L ) is a finite Abelian group under addition modulo the integer lattice Z s , and thatQ L (f) may be written in the form of a nonrepetitive multiple sum,Q L (f) = 1n 1 [ctdot]n m [Sigma ]j 1 =1n 1 [ctdot] [Sigma ]j m = 1 n m f(j 1 n 1 z 1 + [ctdot] + j m n m z m , known as a canonical form, in which + denotes addition modulo Z s . In this form, z i [epsi ] Z s , m is called the rank andn 1 ,n 2 [z.upto]n m are called the invariants ofQ L , and n i + 1 [z.sfnc]n i for i = 1,2[z.upto]m - 1. The rank and invariants are uniquely determined for a given lattice rule. In this paper we provide a construction of a canonical form for a lattice rule Q L , given a generator set for the lattice L. We then show how the rank and invariants of Q L may be determined directly from the generators of the dual lattice L [ p e r p ] .