is a matrix K that can be used to generate the values of a set of treatment factors from a set of blocking factors. Suppose that vector b contains the values of the block factors on a particular unit of the design, and that p is a vector whose *i*th element is the number of levels of treatment factor *i*. (The elements of p should be prime numbers, and usually they are all equal.) Then the vector t containing the values of the treatment factors on that unit of the design is given by

t = `MOD`

( K *+ b; p ).

Often the key is accompanied by a *base vector* v which allows the levels of the factors to be permuted cyclically (this may be useful with quantitative factors). The treatment values are then given by

t = `MOD`

( v + K *+ b; p ).