Technical report Existence of Kirkman signal sets on $v=1,3(\mathrm{mod}6)$ points, $14\le v\le 3000$

Abstract

A partial Steiner triple system whose triples can be partitioned into $s$ partial parallel classes, each of size $m$, is a $signal$ $set$, denoted $\mbox{SS}(v,s,m)$. A $Kirkman$ $signal$ $set$ $\mbox{KSS}(v,m)$ is an $\mbox{SS}(v,s,m)$ with $s=\lfloor \mu (v)/m\rfloor$. When $v\equiv 1$ or $3(\mathrm{mod}6)$, then $\mu (v)=b$, so the decomposition of an $\mbox{STS}(v)$ into partial parallel classes of size $m$ is equivalent to a $\mbox{KSS}(v,m)$. Table of known existence results is given.

51 pages