What are the criteria that the supreme court has adapted in defining strict scrutiny?

The Supreme Court will apply "strict scrutiny" to any law that establishes a quota system in regard to racial (or other) preferences.  Quota systems cannot be used unless it is demonstrated that they are necessary to address past or present patterns of actual discrimination against some persons or groups.  There must be proof that the patterns of actual discrimination have produced or are producing the inequities in regard to how well minorities are represented in a particular area (such as employment, contracts awarded, school admission, etc).  The statistical reality that a minority group is underrepresented somewhere does not in itself prove that there has been discriminatory practice.