## Construction of blocked factorial and fractional factorial designs

**Janet Godolphin (University of Surrey)**

Generating matrix methods are used to construct 2^n and 2^{n-p} factorial designs with single and double confounding, that is, with one or two forms of blocking.

For designs with one form of blocking, the construction of single replicate designs in blocks of size 2^q, enabling estimation of all main effects and maximising the number of estimable two factor interactions is demonstrated. For the situation in which a specific subset of the two factor interactions is of interest, methods on proper vertex colouring from Graph Theory are exploited to inform the generator matrix and yield a suitable design.

Designs with two forms of blocking are represented as one or more rectangular arrays with rows and columns corresponding to blocking factors. Templates are given for generating matrices which yield single replicate constructions to estimate all main effects and the maximum number of two factor interactions.

The construction approaches are extended to accommodate fractional designs.