The Existence of Incomplete Room Squares

Abstract

It has been conjectured by D. R. Stinson that an incomplete Room square $(n,s)$-IRS exists if and only if $n$ and $s$ are both odd and $n\ge 3s+2$, except for the nonexistent case $(n,s)=(5,1)$. In this paper we shall improve the known results and show that the conjecture is true except for $45$ pairs $(n,s)$ for which the existence of an $(n,s)$-IRS remains undecided.