# An infinite family of symmetric designs

- Authors
- Journal
- Discrete Mathematics 0012-365X
- Publisher
- Elsevier
- Publication Date
- Volume
- 26
- Issue
- 3
- Identifiers
- DOI: 10.1016/0012-365x(79)90031-1
- Disciplines

## Abstract

Abstract In this paper, using the construction method of [3], we show that if q>2 is a prime power such that there exists an affine plane of order q−1, then there exists a strongly divisible 2−( q−1)( q h −1), q h −1( q−1), q h −1) design for every h⩾2. We show that these quasi-residual designs are embeddable, and hence establish the existence of an infinite family of symmetric 2−( q h+1 − q+1, q h , q h−1 ) designs. This construction may be regarded as a generalisation of the construction of [1, Chapter 4, Section 1] and [4].

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