  We use our Modified Newtonian Dynamics (MOND) cosmological particle-mesh
N-body code to investigate the feasibility of structure formation in a
framework involving MOND and light sterile neutrinos in the mass range 11 - 300
eV: always assuming that \Omega_{\nu_s}=0.225 for H_o=72 \kms Mpc^{-1}. We run
a suite of simulations with variants on the expansion history, cosmological
variation of the MOND acceleration constant, different normalisations of the
power spectrum of the initial perturbations and interpolating functions. Using
various box sizes, but typically with ones of length 256 Mpc/h, we compare our
simulated halo mass functions with observed cluster mass functions and show
that (i) the sterile neutrino mass must be larger than 30 eV to account for the
low mass (M_{200}<10^{14.6} solar masses) clusters of galaxies in MOND and (ii)
regardless of sterile neutrino mass or any of the variations we mentioned
above, it is not possible to form the correct number of high mass
(M_{200}>10^{15.1} solar masses) clusters of galaxies: there is always a
considerable over production. This means that the ansatz of considering the
weak-field limit of MOND together with a component of light sterile neutrinos
to form structure from z ~ 200 fails. If MOND is the correct description of
weak-field gravitational dynamics, it could mean that subtle effects of the
additional fields in covariant theories of MOND render the ansatz inaccurate,
or that the gravity generated by light sterile neutrinos (or by similar hot
dark matter particles) is different from that generated by the baryons.
