Dualizing with respect to $s$-tuples

Block Designs: A Randomization Approach

“…Then it is easy to see that the parameters are v = k(2k -1), b = 4k2 -1, r = 2k + 1, k = k, .A = 1. Shrikhande (1952) has proved that the the number of s-tuples in a set of the numbers of treatments common to any two blocks in the parent design (see Kageyama and Mohan, 1984b). [Note that if the number of times s-tuples of treatments occur and the number of treatments common to any two blocks in the parent design are not constant, then the values of ki s ) and .xis) are also varying.]…”