The existence of good extensible rank-1 lattices

Abstract

Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h , for extensible rank-1 lattices such that for n= b, b 2,… points and dimensions s=1,2,… the figures of merit R α , P α and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s.