Classicationof associationschemes of small order

This paper enumerates the isomorphism classes of association schemes of order 20 -28 by using the computer. It also classies all the association schemes of order 24 -28 whether their automorphism groups are transitive or not, and whether they are group case or not. Some more properties of the obtained association schemes are computed. c 2002 Elsevier Science B.V. All rights reserved. Using computers, we have been classifying association schemes of small order for the last several years. We classied the isomorphism classes of the associationschemes of order 16 and 17 in (5) and of order 18 and 19 in (6). We also treated primitive associationschemes in( 7). In the present note we classify the isomorphism classes of associationschemes of order up to 28. The n umbers of the isomorphism classes of the associationschemes of order from 16 to 28 are inTable 1. We construct association schemes including all the representatives of the isomorphism classes by using a program writtenin"C". Thenwe compute isomorphisms amon g them by a program writtenin the group algorithm programming language GAP. We also used GAP to develop an algorithm to construct association schemes.