Inequalities for Semiregular Group Divisible Designs

Peter W. M. John

doi:10.1214/aos/1176343592

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Home > Journals > Ann. Statist. > Volume 4 > Issue 5 > Article

September, 1976 Inequalities for Semiregular Group Divisible Designs

Peter W. M. John

Ann. Statist. 4(5): 956-959 (September, 1976). DOI: 10.1214/aos/1176343592

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Abstract

Let $s_{ju}$ be the number of varieties in common to the $j$th and $u$th blocks of a symmetric semiregular group divisible design. Connor (1952) and Saraf (1961) have given inequalities for $s_{ju}$. Both these inequalities lead to the same stronger inequality $\lambda_1 \leqq s_{ju} \leqq 2\lambda_2 - 1$. Both the upper and lower bounds are attained by a series of designs derived from lattices.

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Peter W. M. John. "Inequalities for Semiregular Group Divisible Designs." Ann. Statist. 4 (5) 956 - 959, September, 1976. https://doi.org/10.1214/aos/1176343592