Based on the information provided, the best free MBTI personality test appears to be the TypeFinder test developed by Truity. This test is based on the Myers-Briggs theory and original empirical research, measuring the 4 dimensions and 23 facets of personality type. The results are available online for free, with the option to purchase an expanded report.
The 16Personalities test is another popular free MBTI-based option, however, it has received some criticism regarding its accuracy compared to professionally administered MBTI assessments. In contrast, the TypeFinder test seems to be a more reliable and well-regarded free alternative for those interested in exploring their Myers-Briggs personality type.