Quorums from difference covers

Maekawa considered a simple but suboptimal grid-based quorum generation scheme in which N sites in the network are logically organized in the form of a √N×√N grid, and the quorum sets are row-column pairs. Even though the quorum size 2√N of the grid scheme is twice as large as finite projective plane with optimal sized quorums, it has the advantage of being simple and geometrically evident. Agrawal, Egecioglu, and El Abbadi proposed another grid based scheme producing quorums of size √2N. In this note, a very simple construction is given to produce a system of quorums of size √1.5N. These can be generated efficiently.