Bailey’s Conjecture Holds Through \(87\) Except Possibly for \(64\)

R.A. Bailey has conjectured that all finite groups except elementary Abelian \(2\)-groups with more than one factor have \(2\)-sequencings (i.e., terraces). She verified this for all groups of order \(n\), \(n \leq 9\). Results proved since the appearance of Bailey’s paper make it possible to raise this bound to \(n \leq 87\) with \(n = 64\) omitted. Relatively few groups of order not \(2^n\), \(n \in \{4, 5\}\) must be handled by machine computation.