Optimal designs for an interference model

Kunert and Martin (2000) determined optimal and efficient block designs in a model for field trials with interference effects, for block sizes up to 4. The present paper uses Kushnerʹs (1997) method of finding optimal approximate designs to extend the work of Kunert and Martin (2000) to optimal designs with five or more plots per block. We give an overall upper bound a⁎t,b,k for the trace of the information matrix of any design and show that an universally optimal approximate design will have all its sequences from merely four different equivalence classes. We further determine the efficiency of a binary type I orthogonal array under a general Φ p ‐criterion . We find that these designs achieve high efficiencies of more than 0.94.