Neighbor properties of some classes of BIBRCs and their efficiencies for correlated errors

Some series of previously known balanced incomplete block designs with nested rows and columns are shown to be balanced for neighbors in rows, in columns, and in diagonals when blocks are assumed to be on toruses and/or on cylinders. These series of designs with planar blocks are found to be highly efficient within the class of binary designs when error covariance matrix follows three parameter conditional autonormal process.