Classification of affine resolvable 2-(27, 9, 4) designs

Document Type


Publication Date



All affine resolvable designs with parameters of the design of the hyperplanes in ternary affine 3-space are enumerated. This enumeration implies the classification (up to equivalence), of all optimal equidistant ternary codes of length 13 and distance 9, as well as all complete orthogonal arrays of strength 2 with 3 symbols, 13 constraints and index 3. Up to isomorphism, there are exactly 68 such designs. The automorphism groups and the rank of the incidence matrices over GF(3) are computed. There are six designs with point-transitive automorphism groups, and one design with trivial group. The affine geometry design is the unique design with lowest 3-rank, and the only design with 2-transitive automorphism group.

Publisher's Statement

Copyright © 1996 Published by Elsevier B.V. Publisher’s version of record: https://doi.org/10.1016/S0378-3758(96)00018-3

Corrigendum: https://doi.org/10.1016/S0378-3758(96)00018-3

Publication Title

Journal of Statistical Planning and Inference