## The Annals of Statistics

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

### Inequalities for Semiregular Group Divisible Designs

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62K10: Block designs

**Keywords**

Incomplete block design group divisible semiregular

#### Citation

John, Peter W. M. Inequalities for Semiregular Group Divisible Designs. Ann. Statist. 4 (1976), no. 5, 956--959. doi:10.1214/aos/1176343592. https://projecteuclid.org/euclid.aos/1176343592