In 2011, 2012 and 2013 the Sweet 16 of the NCAA men's Basketball tournament included Marquette, Kansas, Ohio State andFlorida. Therefore, there is no "only team" to achieve this distinction.
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Through 2013, the longest streak of consecutive Sweet 16 appearances in the NCAA men's basketball tournament belongs to North Carolina, which advance to the Sweet 16 for 13 seasons 1981-1993.
From 1967-1980, UCLA was among the final 16 teams, but 1) its 1980 tournament appearance was vacated due to NCAA violations and 2) the tournament did not expand to 32 teams until 1975, effectively negating the concept of "making it to the Sweet 16."
The longest current "streak" belongs to Ohio State, which has been to the Sweet 16 for four straight years (2010-2013).