An Overview of Embedding Problems of Quasi-Residual Designs

The notion of residual and derived design of a symmetric design was introduced in a classic paper by R.C. Bose (1939). A quasi-residual design is a 2-design which has the parameters of a residual design. The embedding problem of quasi-residual design into a symmetric design is an old and natural que...

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Bibliographic Details
Published in:Journal of statistical theory and practice 2009-01, Vol.3 (2), p.319-347
Main Authors: Alraqad, T. A., Shrikhande, M. S.
Format: Article
Language:English
Subjects:
Mathematics and Statistics
Non-embeddable
Probability Theory and Stochastic Processes
Quasi-derived design
Quasi-residual design
Statistical Theory and Methods
Statistics
Symmetric designs
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Summary:The notion of residual and derived design of a symmetric design was introduced in a classic paper by R.C. Bose (1939). A quasi-residual design is a 2-design which has the parameters of a residual design. The embedding problem of quasi-residual design into a symmetric design is an old and natural question. In this survey paper, we discuss various techniques for constructing quasi-residual designs, as well as different types of non-embeddability conditions. We include results for families of non-embeddable quasi-residual designs. Proofs are provided for new results and we give some tables of possible parameter sets of non-embeddable quasi-residual designs.
ISSN:1559-8608
1559-8616
DOI:10.1080/15598608.2009.10411928