Abstract
The theory of (0,1)-matrices plays a fundamental role in many combinatorial investigations. This is especially true in factorial designs where it is desirable to transform, if possible, the design matrix to a (0,1) matrix so that results on (0,1)-matrices can be utilized in solving construction (e.g. optimal designs) and analysis problems. In this connection this paper shows, firstly, that the Anderson-Federer (0,1)-matrix procedure for main effect plans in the general asymmetrical factorial does not extend in a natural way to include plans of a higher degree. Secondly, a transformation is provided, in the case of the symmetrical factorial, which converts design matrices defined relative to a suitable class of observation vectors and admissible sets of effects of degree at most two which include the mean into (0,1)-matrices. Further a transformation is given which converts any design matrix relative to an admissible set of effects into a (-l,0,l)-matrix.
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