The exact equations governing the narrow-band resolution and detection capabilities of conventional (CONV) and minimum energy (ME) adaptive beamforming [1], are the basis for a class of linear arrays which offers simultaneously optimum resolution and detection capacities. Signal processing considerations indicate that, in this class, linear minimum redundancy (LMR) arrays [2] are best suited to CONV beamforming, and linear minimum hole (LMH) arrays [3] are best suited to minimum energy (ME) beamforming. The effect of coarray redundancies and holes on sidelobe level is examined analytically, and lower bounds are established on the number of coarray redundancies and holes. A simple recursive algorithm for the design of LMH arrays is presented.