AbstractWilson's construction for mutually orthogonal Latin squares is generalized. This generalized construction is used to improve known bounds on the function nr (the largest order for which there do not exist r MOLS). In particular we find n7⩽780, n8⩽4738, n9⩽5842, n10⩽7222, n11⩽7478, n12⩽9286, n13⩽9476, n15⩽10632