  We investigate a frustrated Ising spin system on the garnet lattice composed
of a specific network of corner-sharing triangles. By means of Monte Carlo
simulations with the heat bath algorithm, we discuss the magnetic properties at
finite temperatures. It is shown that the garnet spin system with the
nearest-neighbor couplings does not exhibit any magnetic transitions, yielding
the large residual entropy at zero temperature. We also investigate the effect
of the long-range dipolar interaction systematically to determine the phase
diagram of the Ising model on the garnet lattice. We find that there appear a
variety of distinct phases depending on the cutoff length of the long-range
interaction, in contrast to the pyrochlore spin-ice systems.
