Construction of Efficient Multi-Level k-Circulant Supersaturated Designs

Abstract

This article proposes an algorithm to construct efficient balanced multi-level k-circulant supersaturated designs with m factors and n runs. The algorithm generates efficient balanced multi-level k-circulant supersaturated designs very fast. Using the proposed algorithm many balanced multi-level supersaturated designs are constructed and cataloged. A list of many optimal and near optimal, multi-level supersaturated designs is also provided for m ≤ 60 and number of levels (q) ≤10. The algorithm can be used to generate two-level k-circulant supersaturated designs also and some large optimal two-level supersaturated designs are presented. An upper bound to the number of factors in a balanced multi-level supersaturated design such that no two columns are fully aliased is also provided.

Keywords:

• Algorithm
• Aliased
• Efficiency
• k-circulant
• Multi-level
• Supersaturated designs

Mathematics Subject Classification:

• 62K15

Acknowledgments

The authors are grateful to the two reviewers and Associate Editor for giving valuable suggestions that helped to improve the presentation of this article.

Notes

(Continued)