There has never been a verifiably perfect March Madness bracket in the history of the NCAA tournament, which might be due to the fact that the general consensus among mathemeticians puts the odds of attaining a perfect bracket at one in 9.2 quintillion.
Since 2011, the big dance has had 68 teams competing in its field since 2011. Eight of those teams compete in the “First Four," or play-in games that take place before the first round of the tournament. Almost all bracket pools disregard these games and only count games starting with the official first round of March Madness, when 64 teams tip off.
Beginning with the first round through the championship, there are 63 games in a standard NCAA tournament bracket that an individual would have to predict correctly to make a perfect bracket.
Assuming that the odds of picking each game correctly are an even 50-50–like a coin flip–the number of possible bracket outcomes is 9,223,372,036,854,775,808. Given the overwhelming odds against predicting every single upset in the madness that is March basketball, it's not surprising that the feat has not been accomplished yet.