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The application of Minnick and Ashenhurst's technique of p-fold multiple-coincidence magnetic storage in an n x n array of cores is shown to require finding (p-2) orthogonal Latin squares of order n. The value of this technique lies in the reduction it effects in the disturbance of unselected cores. A method is suggested for reducing this disturbance to a level lower than that obtained by Minnick and Ashenhurst, by the application of reverse currents to the unselected interrogating wires during interrogation. The disturbance of unselected cores can be reduced to zero if p=n+1. In this case, (n+1) cores can be added to the store at the expense of a single additional interrogating wire. The resulting array of cores and interrogating wires is closely related to the finite projective geometry of order n.