  MACHe3 (MAtrix of Cells of superfluid He3) is a project of a new detector for
direct Dark Matter (DM) search. A cell of superfluid He3 has been developed and
the idea of using a large number of such cells in a high granularity detector
is proposed. This paper presents, after a brief description of the superfluid
He3 cell, the simulation of the response of different matrix configurations
allowing to define an optimum design as a function of the number of cells and
the volume of each cell. The background rejection, for several configurations,
is presented both for neutrons and gamma-rays of various kinetic energies.
