## The Annals of Statistics

### On a New Type of $m$-Class Cyclic Association Scheme and Designs Based on the Scheme

#### Abstract

A new type of $m$-class cyclic association scheme is defined for $v$ objects, where $v$ is either a prime or power of a prime. The two cases, when $v$ is even and when $v$ is odd are dealt with separately. A simple method of construction of PBIB designs based on this scheme is proposed. The PBIB designs presented in this paper have cyclic solutions and are obtainable through more than one initial block. The proposed scheme has been called an $NC_m$ association scheme and the number of independent $p_{jk}$'s for this scheme is obtained.

#### Article information

Source
Ann. Statist., Volume 1, Number 5 (1973), 985-990.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176342521

Digital Object Identifier
doi:10.1214/aos/1176342521

Mathematical Reviews number (MathSciNet)
MR433755

Zentralblatt MATH identifier
0274.62055

JSTOR
Saha, G. M.; Kulshreshtha, A. C.; Dey, A. On a New Type of $m$-Class Cyclic Association Scheme and Designs Based on the Scheme. Ann. Statist. 1 (1973), no. 5, 985--990. doi:10.1214/aos/1176342521. https://projecteuclid.org/euclid.aos/1176342521