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Original Articles

Efficient Incomplete Block Designs Through Linear Integer Programming

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SYNOPTIC ABSTRACT

The purpose of this paper is to present a linear integer programming approach to construct efficient binary incomplete block designs for any given number of treatments v, number of blocks b, with common block-size k, and with a nearly balanced concurrence matrix. The proposed approach is illustrated by constructing an efficient incomplete block design. A-efficient and D-efficient incomplete block designs have been constructed and catalogued using the proposed algorithm for a restricted range of parameters 3 ⩽ v ⩽ 20, bv, and 2 ⩽ k ⩽ min(10, v − 1), with vb⩽1, 000. An R package is developed to implement the proposed approach.

Acknowledgments

The authors are grateful to two anonymous reviewers and the Associate Editor for making valuable suggestions that have improved the presentation of this article.

Notes

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