  (abriged) Stellar clusters with the same general physical properties (e.g.,
total mass, age, and star-formation mode) may have very different stellar mass
spectra due to the incomplete sampling of the underlying mass function; such
differences are especially relevant in the high-mass tail due to the smaller
absolute number of massive stars. The dispersion in the number of massive stars
also produces a dispersion in the properties of the corresponding ionising
spectra. In this paper, we lay the bases for the future analysis of this effect
by evaluating the dispersion in the ionising fluxes of synthetic spectra. As an
important consequence, we found that the intensities of synthetic fluxes at
different ionisation edges are strongly correlated, a fact suggesting that no
additional dispersion will result from the inclusion of sampling effects in the
analysis of diagnostic diagrams; this is true for HII regions on all scales.
Additionally, we find convincing suggestions that the He II lines are strongly
affected by sampling, and so cannot be used to constrain the evolutionary
status of stellar clusters. We also establish the range of applicability of
synthesis models set by the Lowest Luminosity Limit for the ionising flux, that
is the lowest limit in cluster mass for which synthesis models can be applied
to predict ionising spectra. This limit marks the boundary between the
situations in which the ionising flux is better modeled with a single star as
opposed to a star cluster; this boundary depends on the metallicity and age,
ranging from 10^3 to more than 10^6 Mo. As a consequence, synthesis models
should not be used to try to account for the properties of clusters with
smaller masses.
