Block-Transitive Designs in Affine Spaces

Abstract

This paper deals with block-transitive $t$-$(v,k,\lambda )$ designs in affine spaces for large $t$, with a focus on the important index $\lambda =1$ case. We prove that there are no non-trivial 5-$(v,k,1)$ designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-$(v,k,1)$ designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.

10 pages; to appear in: "Designs, Codes and Cryptography"

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• On the Cameron-Praeger Conjecture
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