Row-column factorial designs of strength at least 2

Speaker: Nicholas Cavenagh
Affiliation: University of Waikato, New Zealand

Abstract

The q^k (full) factorial design with replication lambda is the multi-set consisting of lambda occurrences of each element of each q-ary vector of length k; we denote this by lambda times [q]^k. 

An m times n row-column factorial design q^k of strength t is an arrangement of the elements of lambda times [q]^k into an m times n array (which we say is of type I_k(m,n,q,t))  such that for each row (column), the set of vectors there in are the rows of an orthogonal array of size k, degree n (respectively, m), q levels and strength t. 

Such arrays have been used in practice in experimental design. 

In this context, for a row-column factorial design of strength t, all subsets of interactions of size at most t can be estimated without confounding by the row and column blocking factors.

In this talk we consider row-column factorial designs with strength t>= 2.   The constructions presented uses Hadamard matrices and linear algebra.