A multibeamlet approach to a high current ion injector, whereby a large number of beamlets are accelerated and then merged to form a single beam, offers a number of potential advantages over a monolithic single beam injector. These advantages include a smaller transverse footprint, more control over the shaping and aiming of the beam, and more flexibility in the choice of ion sources. A potential drawback, however, is a larger emittance. In this paper, we seek to understand the merging of the beamlets and how it determines the emittance. When the constraints imposed by beam propagation physics and practical engineering issues are included, the design is reduced to a few free parameters. We describe the physics design of a multibeamlet injector and produce a design for an example set of parameters. Extensive use of 2D and 3D particle simulations was made in understanding the injector. Design tolerances and sensitivities are discussed in general and in relation to the example.