The Alias Matrix entries represent the degree of bias imparted to model parameters by the effects that you specified in the Alias Terms outline. Calculations for the Alias Matrix are based on the model matrix. See The Model Matrix.
Let X1 be the model matrix corresponding to the terms in the Model outline. Denote the matrix of model terms for the effects specified in the Alias Terms outline by X2.
where V is the block diagonal covariance matrix of the responses.
where K is a diagonal matrix with these values:
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k = 0 for Necessary terms

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k = 1 for If Possible main effects, powers, and interactions involving a categorical factor with more than two levels

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k = 4 for all other If Possible terms

In the Bayesian case, the alias matrix gives the aliasing of effects corresponding to a ridge regression with a prior variance of . For additional detail on Bayesian designs, see Bayesian DOptimality in Custom Designs and Bayesian IOptimality in Custom Designs.
In the Custom Design platform, you can control the weights used for If Possible terms by selecting Advanced Options > Prior Parameter Variance from the red triangle menu. There you can set prior variances for all model terms by specifying the diagonal elements of K. The option updates to show the default weights when you click Make Design.