A recent result of Schmidt has brought Williamson matrices back into the spotlight. In this paper a new algorithm is introduced to search for hard to find Williamson matrices. We find all nonequivalent Williamson matrices of odd order n up to n = 59. It turns out that there are none for n = 35, 47, 53, 59 and it seems that the Turyn class may be the only infinite class of these matrices. AMS Su...
