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P. J. Federico used the term low-order for perfect squared squares with atmost 28 squares in their dissection. In 2010 low-order compound perfect squaredsquares (CPSSs) were completely enumerated. Up to symmetries of the square andits squared subrectangles there are 208 low-order CPSSs in orders 24 to 28. In2012 the CPSSs of order 29 were completely enumerated, giving a total of 620CPSSs up to order 29.

Compound Perfect Squared Squares of the Order Twenties