  Quasi-Monte Carlo methods have proven to be effective extensions of
traditional Monte Carlo methods in, amongst others, problems of quadrature and
the sample path simulation of stochastic differential equations. By replacing
the random number input stream in a simulation procedure by a low-discrepancy
number input stream, variance reductions of several orders have been observed
in financial applications.
  Analysis of stochastic effects in well-mixed chemical reaction networks often
relies on sample path simulation using Monte Carlo methods, even though these
methods suffer from typical slow $\mathcal{O}(N^{-1/2})$ convergence rates as a
function of the number of sample paths $N$. This paper investigates the
combination of (randomised) quasi-Monte Carlo methods with an efficient sample
path simulation procedure, namely $\tau$-leaping. We show that this combination
is often more effective than traditional Monte Carlo simulation in terms of the
decay of statistical errors. The observed convergence rate behaviour is,
however, non-trivial due to the discrete nature of the models of chemical
reactions. We explain how this affects the performance of quasi-Monte Carlo
methods by looking at a test problem in standard quadrature.
