Construction of Balanced Incomplete Block Designs Using Cyclic Shifts

The construction of balanced incomplete block designs is considered using the method of cyclic shifts. An interesting feature of this method is that there is no need to construct the bocks of the actual design to obtain the properties of a design. One can obtain the off-diagonal elements of the concurrence matrix from the sets of shifts with less effort. A catalogue of balanced incomplete block designs for 3 ≤ v ≤ 18 with k = v -1, 19 ≤ v ≤ 100 with k = 2, 3 and for 19 ≤ v ≤ 25 with k = 4, 5 restricted with r < 60 is compiled.