A Note on Embedding Partial Extended Triple Systems of Even Index

Abstract

Recently, Raines and Rodger have proved that for all $\lambda \ge 1$, any partial extended triple system of order $n$ and index $\lambda$ can be embedded in a (complete) extended triple system of order $v$ and index $\lambda$ for any even $v\ge 4n+6$. In this note, it is shown that if $\lambda$ is even then this bound on $v$ can be improved to all $v\ge 3n+5$, and under some conditions to all $v\ge 2n+1$.