Two-level supersaturated designs for runs and other cases

Two-level supersaturated designs are constructed for n = 2 k ( k ⩾ 5 ) runs and m factors where n + 3 ⩽ m ⩽ 5 ( n - 4 ) . The designs so formed are shown to have a maximum absolute correlation between factors of 1 4 and to be efficient in terms of E ( s 2 ) , particularly when the number of factors m is approximately double the number of runs n or greater. Thus, supersaturated designs with favourable properties are found for much higher numbers of runs than would be possible solely using algorithms.