Abstract
Two-dimensional lattice rules are applied to continuous functions over the unit square which do not have a continuous periodic extension. It is shown that, provided lattice points at vertices and edges are treated appropriately, certain functions (including all bilinear functions) are integrated exactly whenever the lattice contains a (possibly rotated) square unit cell. The Fibonacci lattice with denominators F k for the nodes is then shown to have a square unit cell if and only if k is odd. Numerical experiments for Fibonacci rules and copies of Fibonacci rules confirm that there are significant different between the odd- k and even- k cases.
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