Maximum estimation capacity projection designs from Hadamard matrices with 32, 36 and 40 runs

An important problem in experimental procedures is the selection of the appropriate design. A design with generalized minimum aberration (GMA) is often considered the best. However, other designs might suit better practical needs, especially when two factor interactions (2fis) are of interest. Here we find all the inequivalent projection designs from Hadamard matrices of order 32, 36 and 40 into q=3,4,5q=3,4,5 factors and order 32 into 6 factors and we study them according to their ability to estimate as many 2fis as possible with the greatest efficiency. We also present the maximum estimation capacity (EC) designs when considering 2 and 3 factor interactions. Furthermore, we give the best GMA designs and examine their connection with those having maximum EC.