Serially balanced sequences of types 1 and 2 are used for designing experiments where one experimental unit receives several treatments over successive periods. Both the direct effect of a treatment applied in a certain period, as well as the residual effect of the treatment applied in the previous period, are of interest. Optimality properties of such sequences have been studied in the literature. However, these sequences have block sizes equal to the number of treatments v and so they pose a problem to the practitioner when v is large. In this paper, a class of sequences with incomplete blocks is proposed and their construction and analysis given. These sequences can be used to estimate direct and residual effects of treatments with high efficiencies. The sequences may be replicated over any number of units when the experiment is run with more than one unit.

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