The 1-rotational Kirkman triple systems of order 33

Abstract

We establish that there are exactly 500 KTS(33)s admitting an automorphism group fixing one point and acting regularly on the remainder; 436 are over the cyclic group while 64 are over the dicyclic group. There are exactly 243 nonisomorphic STS(33)s underlying the above KTS(33)s; 211 are over the cyclic group while 32 are over the dicyclic group. This gives a significant improvement on the number of known KTS(33)s (at least 528 instead of at least 28).