Abstract
Every lattice rule in s dimensions may be characterised by an integer m, lying between 1 and s inclusive, called the rank or index of the rule and a set of m positive integers called the invariants. Earlier work has shown that, in a certain precise sense, lattice rules of rank s are better than the commonly used rank-1 rules. Here this earlier work is extended by showing that a similar result holds for certain lattice rules of intermediate rank $m < s$.
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