  Multimaterial optical coatings are a promising viable option to meet the
challenging requirements (in terms of transmittance, absorbance and thermal
noise) of next generation gravitational wave detector mirrors. In this paper we
focus on ternary coatings consisting of quarter-wavelength thick layers, where
a third material (H') is added to the two presently in use, namely Silica (L)
and Titania-doped Tantala (H), featuring higher dielectric contrast (against
Silica), and lower thermal noise (compared to Titania-doped Tantala), but
higher optical losses. We seek the optimal material sequences, featuring
minimal thermal (Brownian) noise under prescribed transmittance and absorbance
constraints, by exhaustive simulation over all possible configurations, for
different values (in a meaningful range) of the optical density and extinction
coefficient of the third material. In all cases studied, the optimal designs
consist of a stack of (H'|L) doublets topped by a stack of (H|L) doublets,
confirming previous heuristic assumptions, and the achievable coating noise
power spectral density reduction factor is \sim 0.5. The robustness of the
found optimal designs against layer thickness deposition errors and
uncertainties and/or fluctuations in the optical losses of the third material
is also investigated. Possible margins for further thermal noise reduction by
layer thickness optimization, and strategies to implement it, are discussed.
