Maximal Triangle Trades with Foundation $5(\mathrm{mod}6)$ — the Final Case

Abstract

The maximum possible volume of a simple, non-Steiner $(v,3,2)$ trade was determined for all $v$ by Khosrovshahi and Torabi (Ars Combinatoria $51(1999),211-223)$; except that in the case $v\equiv 5$ (mod 6), $v\ge 23$, they were only able to provide an upper bound on the volume. In this paper we construct trades with volume equal to that bound for all $v\equiv 5$ (mod 6), thus completing the problem.