The number of lattice rules
The authors determine the number \(\nu_ s(N)\) of distinct N-point S- dimensional lattice rules. First, it is established that \(\nu_ s(MN)\leq \nu_ s(M)\nu_ s(N)\) equality being attained if and only if M and N are mutually prime; then this is used to establish that, when L has prime factor expansion \(\prod_{j}p_ j^{t_ j}\), then \(\nu_ s(L)=\prod_{j}\nu_ s(p_ j^{t_ j})\) where \(\nu_ s=\prod^{S- 1}_{i=1}[(p^{i+t}-1)/(p^ i-1)];\quad S\geq 1,\quad t\geq 0.\)
scientific article; zbMATH DE number 4113839