Sound fields are essentially band-limited phenomena, both temporally and spatially. This implies that a spatially sampled sound field respecting the Nyquist criterion is effectively equivalent to its continuous original. We describe Sound Field Reconstruction (SFR)---a technique that uses the previously stated observation to express the reproduction of a continuous sound field as an inversion of the discrete acoustic channel from a loudspeaker array to a grid of control points. The acoustic channel is inverted using truncated singular value decomposition (SVD) in order to provide optimal sound field reproduction subject to a limited effort constraint. Additionally, a detailed procedure for obtaining loudspeaker driving signals that involves selection of active loudspeakers, coverage of the listening area with control points, and frequency domain FIR filter design is described. Extensive simulations comparing SFR with Wave Field Synthesis show that on average, SFR provides higher sound field reproduction accuracy.