  Photonic crystal nanobeam cavities are versatile platforms of interest for
optical communications, optomechanics, optofluidics, cavity QED, etc. In a
previous work \cite{quan10}, we proposed a deterministic method to achieve
ultrahigh \emph{Q} cavities. This follow-up work provides systematic analysis
and verifications of the deterministic design recipe and further extends the
discussion to air-mode cavities. We demonstrate designs of dielectric-mode and
air-mode cavities with $Q>10^9$, as well as cavities with both high-\emph{Q}
($>10^7$) and high on-resonance transmissions ($T>95%$).
