**Systematic PPS sampling (PPSSYS)**

In this method, the properties of systematic sampling and sampling proportional to size are combined into a single sampling scheme. In ordinary systematic sampling, the sampling interval is determined by the quotient q = N/n. In systematic PPS sampling, the sampling interval is given by q = Tz/n. As in the ordinary onerandom- start systematic sampling, we first select a random number from the closed interval [1, q]. See pages 51-52 in Lehtonen, R & Pahkinen, E. (2004)