This paper emphasize the binary population: CMD fitting with the binary population synthetic model outperformed to the single population model. They used Hurley code (Hurley, Tout, and Pols (2002). Evolution of binary stars and the effect of tides on binary populations, MNRAS, 329(4), p.897-928). They mentioned that two color-color grids can disentangle the age-metallicity degeneracy via binary stellar populations. They fitted their isochrone database to M67 and NGC 1868 with the gT-grid and concluded that the database of binary stellar populations fitted the color magnitude diagrams better.

A notable sentence:

According to the work of Li and Han (2007b, arxiv/astro-ph: 0704.1202), (u-R) and (g-J) are sensitive to stellar age while (r-K) and (z-K) to stellar metallicity,

where the upper cases indicate Johnson UBVRIJHK magnitudes and the lower cases SDSS-ugriz magnitudes.

I rather skip all technical details on ultracool dwarfs and binary stars, reviews on star formation studies, like initial mass function (IMF), astronomical survey studies, which Allen gave a fair explanation in arxiv/astro-ph:0707.2064v1 but want to emphasize that based on simple Bayes’ rule and careful set-ups for likelihoods and priors according to data (ultracool dwarfs), quite informative conclusions were drawn:

1. the peak at q~1 is significant,
2. lack of companions with a distance greater than 15-20 A.U. (a unit indicates the distance between the Sun and the Earth),
3. less binary stars with later spectral types,
4. inconsistency of undetected low mass ratio systems to the current data, and
5. 30% spectroscopic binaries are from ultracool binaries.

Before, asking for observational efforts for improvements, it is commented 75% as the the upper limit of the ultracool binary population.