CONSTRUCTION OF 5-HELIX SYSTEMS OF INDEX 2

Abstract

A $5$-\emph{helix} $S^{(3)}(1,5)$ of \emph{centre} $\{c\}$ is a {3-uniform} hypergraph, with 5 hyperedges, all having in common exactly the \emph{centre} $\{c\}$ of degree 5, and the remaining vertices of degree 1. In this paper we determine the spectrum of {$S^{(3)}(1,5)$-\emph{designs}} of index 2 with pairwise distinct blocks.