A new recursive construction for large sets of Kirkman triple systems

We give a recursive construction of an LKTS(7q + 2) from an LKTS(q + 2) and an auxiliary permutation structure on an abelian group of order q, which we call a cubic orthomorphism.

We prove that cubic orthomorphisms exist whenever q is a product of prime powers congruent to 1 modulo 6.

The construction yields, in particular, LKTSs of orders 93, 177, 219, 261, and 303.