Exact, Uniform Sampling of Latin Squares and Sudoku Matrices

We provide a method for the exact, uniform random sampling of Latin squares and Sudoku matrices via probabilistic divide-and-conquer. Using an implementation in C++, we have generated i.i.d. samples of size 1000 each of Sudoku matrices and Latin Squares of order $n$, $5 \leq n \leq 9.$