Designs, Codes and Cryptography

, Volume 48, Issue 3, pp 287–292

# On orthogonal resolutions of the classical Steiner quadruple system SQS(16)

• Hans Ludwig de Vries
Open Access
Article

## Abstract

A Steiner quadruple system SQS(16) is a pair $${(V, \mathcal{B})}$$ where V is a 16-set of objects and $${\mathcal B}$$ is a collection of 4-subsets of V, called blocks, so that every 3-subset of V is contained in exactly one block. By classical is meant the boolean quadruple system, also known as the affine geometry AG(4,2). A parallel class is a collection of four blocks which partition V. The system possesses a resolution or parallelism, since $${\mathcal B}$$ can be partitioned into 35 parallel classes. Two resolutions are called orthogonal when each parallel class of one resolution has at most one block in common with each parallel class of the other resolution. We prove that there are at most nine further resolutions which, together with the classical one, are pairwise orthogonal.

## Keywords

Steiner quadruple system Automorphism group Resolutions

## AMS Classifications

05B05 05B07 51E10

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## Authors and Affiliations

1. 1.Institut für Numerische und Angewandte MathematikGeorg-August-Universität GöttingenGöttingenGermany