文摘
We enumerate three classes of non-medial quasigroups of order 243=35243=35 up to isomorphism. There are 17004 non-medial trimedial quasigroups of order 243243 (extending the work of Kepka, Bénéteau and Lacaze), 9292 non-medial distributive quasigroups of order 243243 (extending the work of Kepka and Němec), and 66 non-medial distributive Mendelsohn quasigroups of order 243243 (extending the work of Donovan, Griggs, McCourt, Opršal and Stanovský).The enumeration technique is based on affine representations over commutative Moufang loops, on properties of automorphism groups of commutative Moufang loops, and on computer calculations with the LOOPS package in GAP.