  Continuous level Monte Carlo is an unbiased, continuous version of the
celebrated multilevel Monte Carlo method. The approximation level is assumed to
be continuous resulting in a stochastic process describing the quantity of
interest. Continuous level Monte Carlo methods allow naturally for samplewise
adaptive mesh refinements, which are indicated by goal-oriented error
estimators. The samplewise refinement levels are drawn in the estimator from an
exponentially-distributed random variable. Unfortunately in practical examples
this results in higher costs due to high variance in the samples. In this paper
we propose a variant of continuous level Monte Carlo, where a quasi Monte Carlo
sequence is utilized to "sample" the exponential random variable. We provide a
complexity theorem for this novel estimator and show that this results
theoretically and practically in a variance reduction of the whole estimator.
