## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 398-407.

### An Upper Bound for the Number of Disjoint Blocks in Certain PBIB Designs

#### Abstract

Majinder [3] obtained an upper bound for the number of disjoint blocks in BIB designs. In this paper we give an upper bound for the number of disjoint blocks in (i) Semi-regular GD designs, (ii) PBIB designs with two associate classes having triangular association scheme, (iii) PBIB designs with two associate classes having $L_2$ association scheme, and (iv) PBIB designs with three associate classes having rectangular association scheme. The main tools used to establish the results of this paper are the theorems proved by (i) Bose and Connor [1], (ii) Raghavarao [4] and (iii) Vartak [6].

#### Article information

**Source**

Ann. Math. Statist., Volume 35, Number 1 (1964), 398-407.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177703763

**Digital Object Identifier**

doi:10.1214/aoms/1177703763

**Mathematical Reviews number (MathSciNet)**

MR158492

**Zentralblatt MATH identifier**

0138.14105

**JSTOR**

links.jstor.org

#### Citation

Shah, S. M. An Upper Bound for the Number of Disjoint Blocks in Certain PBIB Designs. Ann. Math. Statist. 35 (1964), no. 1, 398--407. doi:10.1214/aoms/1177703763. https://projecteuclid.org/euclid.aoms/1177703763