The operad of Latin hypercubes

Abstract We show that the sets of $d$ -dimensional Latin hypercubes over a non-empty set $X$ , with $d$ running over the positive integers, determine an operad which is isomorphic to a sub-operad of the endomorphism operad of $X$ . We generalise this to categories with finite products, and then further to internal versions for certain Cartesian closed monoidal categories with pullbacks.