In a series of papers, in 1993, 1994 & 1996 (see [NS93,NS94,NS96]), Ian Sloan together with Harald Niederreiter introduced a modification of lattice rules for non-periodic functions, called ``vertex modified lattice rules'', and a particular breed called ``optimal vertex modified lattice rules''.These are like standard lattice rules but they distribute the point at the origin to all corners of the unit cube, either by equally distributing ...