Known series of balanced incomplete block designs with nested rows and columns are used to find orthogonal sets of these designs, producing main effects plans in nested rows and columns. Two infinite series are so constructed and shown to be universally optimum for the analysis with recovery of row and column information, a benefit produced by the additional higher strata orthogonality they enjoy. One of these series achieves orthogonality with just v - 1 replicates ofv treatments, fewer than required by Latin squares.