## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 408-414.

### On a Bound Useful in the Theory of Factorial Designs and Error Correcting Codes

R. C. Bose and J. N. Srivastava

#### Abstract

Consider a finite projective space $PG(r - 1, s)$ of $r - 1$ dimensions, $r \geqq 3$, based on the Galois field $GF_s$, where $s = p^h, p$ being a prime. A set of distinct points in $PG(r - 1, s)$ is said to be a non-collinear set, if no three are collinear. The maximum number of points in such a non-collinear set is denoted by $m_3(r, s)$. It is the object of this paper to find a new upper bound for $m_3(r, s)$. This bound is of importance in the theory of factorial designs and error correcting codes. The exact value of $m_3(r, s)$ is known when either $r \leqq 4$ or when $s = 2$. When $r \geqq 5, s > 3$, the best values for the upper bound on $m_3(r, s)$ are due to Tallini [10] and Barlotti [1]. Our bound improves these when $s = 3$ or when $s$ is even.

#### Article information

**Source**

Ann. Math. Statist., Volume 35, Number 1 (1964), 408-414.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177703764

**Digital Object Identifier**

doi:10.1214/aoms/1177703764

**Mathematical Reviews number (MathSciNet)**

MR159399

**Zentralblatt MATH identifier**

0124.11503

**JSTOR**

links.jstor.org

#### Citation

Bose, R. C.; Srivastava, J. N. On a Bound Useful in the Theory of Factorial Designs and Error Correcting Codes. Ann. Math. Statist. 35 (1964), no. 1, 408--414. doi:10.1214/aoms/1177703764. https://projecteuclid.org/euclid.aoms/1177703764