## The Annals of Mathematical Statistics

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

S. M. Shah

#### 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

#### 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