## The Annals of Statistics

### Inequalities for Semiregular Group Divisible Designs

Peter W. M. John

#### 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.

#### Article information

Source
Ann. Statist., Volume 4, Number 5 (1976), 956-959.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343592

Digital Object Identifier
doi:10.1214/aos/1176343592

Mathematical Reviews number (MathSciNet)
MR419256

Zentralblatt MATH identifier
0357.62055

JSTOR