Construction of supersaturated designs through partially aliased interactions

An N × N Hadamard matrix can be used to construct a saturated 2 N−1design with N runs. Furthermore, if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix, this interaction column can be used as a supplementary column for studying an additional factor. For some small Hadamard matrices studied by Plackett & Burman (1946), the number of such interaction columns is very large, thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs. A general method of construction along these lines is proposed. The efficiency of the constructed designs is studied by using three criteria.