columns. The resulting matrix, minus that column, is a "supersaturated design" for finding significant first order effects, under the assumption that few exist. Box–Behnken designs can be made smaller, or very large ones constructed, by replacing the fractional factorials and incomplete blocks traditionally used for plan and seed matrices, respectively, with Plackett–Burmans. For example, a quadratic design for 30 variables requires a 30 column PB plan matrix of zeroes and ones, replacing the ones in each line using PB seed matrices of −1s and +1s (for 15 or 16 variables) wherever a one appears in the plan matrix, creating a 557 runs design with values, −1, 0, +1, to estimate the 496 parameters of a full quadratic model. Adding axial points allows estimating univariate cubic and quartic effects. By equivocating certain columns with parameters to be estimated, Plackett–Burmans can also be used to construct mixed categorical and numerical designs, with interactions or high order effects, requiring no more than 4 runs more than the number of model parameters to be estimated. Sort by a-1 columns assigned to categorical variable A and following columns, where A = 1 + int(a·i /(max(i) + 0.00001)), i = row number and a = A's number of values. Next sort on columns assigned to any other categorical variables and following columns, repeating as needed. Such designs, if large, may otherwise be incomputable by standard search techniques like D-optimality. For example, 13 variables averaging 3 values each could have well over a million combinations to search. To estimate the 105 parameters in a quadratic model of 13 variables, one must formally exclude from consideration or compute |X'X| for well over 106C102, i.e. 313C105, or roughly 10484 matrices. 4 to 48 runs, sorted to show half-fractions P.B.4 + + + + – – – + – – – + P.B.8 + + + + + + + + + – – – – + + – + + – – – + – – – + + – – + + – + – – – + – + – + – – – + – – + + – – – + + – + P.B.12 + + + + + + + + + + + + + + + – – – + – – – + + – – – + – – + – + + – + – + + +