On the Yeh-Bradley Conjecture on Linear Trend-Free Block Designs

Abstract

Yeh and Bradley conjectured that every binary connected block design with blocks of size $k$ and a constant replication number $r$ for each treatment can be converted to a linear trend-free design by permuting the positions of treatments within blocks if and only if $r(k + 1) \equiv 0 (\operatorname{mod} 2)$. This conjecture is studied. Results include: (i) the conjecture is true whenever the block size is even and (ii) the conjecture is true for BIB designs.