A method for constructing quasimultiple affine planes of arbitrary order
The authors consider the problem of constructing quasimultiple designs of an affine plane of an arbitrary order \(n\) (even if no such plane exists), i.e. the existence problem for \((n^ 2, n, n\lambda)\)-designs. In this context, it is of interest to determine the smallest such \(\lambda\), a problem considered by the reviewer in his paper [``On the existence of small quasimultiples of affine and projective planes of arbitrary order'', Discrete Math. 85, No. 2, 177-189 (1990; Zbl 0729.05009)]. The present authors give a construction using 2-transitive groups which allows them to obtain several improvements on the previously known bounds; in particular, a quasidouble (i.e. \(\lambda= 2\)) is obtained for \(n= 28\).
scientific article; zbMATH DE number 759429