Lattice rules of minimal and maximal rank with good figures of merit (Q1964083)

The error of numerical cubature of periodic functions in \(s\) dimensions by lattice rules can be estimated in terms of the so-called figure of merit \(\rho\). The problem of finding good rules having \(N\) distinct nodes can therefore conveniently be reduced to that of finding rules with large values of \(\rho\). In the paper under review a method is described for the systematic search for (in this sense) best rules among rules of rank 1 and among \(2^s\) copies of rank 1 rules. Some additions and corrections for tables of optimal rank 1 rules published previously by other authors are given. Tables for optimal \(2^s\) copy rules are included for dimensions \(s=3,4,5\) and \(N< 16 000\).