  We discuss relations between two different representations of hypothetical
holomorphic NSR measures, based on two different ways of constructing the
semi-modular forms of weight 8. One of these ways is to build forms from the
ordinary Riemann theta constants and another -- from the lattice theta
constants. We discuss unexpectedly elegant relations between lattice theta
constants, corresponding to 16-dimensional self-dual lattices, and Riemann
theta constants and present explicit formulae expressing the former ones
through the latter. Starting from genus 5 the modular-form approach to
construction of NSR measures runs into serious problems and there is a risk
that it fails completely already at genus 6.
