Sarvate-Beam Quad Systems for $v=6$

Abstract

A Sarvate-Beam Quad System $SB(v,4)$ is a set $V$ of $v$ elements and a collection of $4$-subsets of $V$ such that each distinct pair of elements in $V$ occurs $i$ times for every $i$ in the list $1,2,\dots ,(\genfrac{}{}{0ex}{}{v}{2})$. In this paper, we completely enumerate all Sarvate-Beam Quad Systems for $v=6$.