Established methods for synthesising a population from geographically aggregated data are robust and well understood. However, most rely on the potentially detrimental process of integerisation if a whole individual population is required, e.g. for use in agent-based modelling (ABM). This paper describes and investigates the use of quasirandom sequences to sample populations from known marginal constraints whilst preserving those marginal distributions. We call this technique Quasirandom Integer Without-replacement Sampling (QIWS) and show that the statistical properties of quasirandomly sampled populations to be superior to those of pseudorandomly sampled ones in that they tend to yield entropies much closer to populations generated using the entropy-maximising iterative proportional fitting (IPF) algorithm. The implementation is extremely efficient, easily outperforming common IPF implementations. It is freely available as an open source R package called humanleague. Finally, we suggest how the current limitations of the implementation can be overcome, providing a direction for future work.