Abstract :
Recently, Gonzalez-Dorrego has given a list of 9 different ways of constructing a nondegenerate (16, 6) configuration from a group of order 16 (up to automorphisms and translations of the group). In this paper, using her algorithm with a minor correction, we obtain 27 such constructions, completing the list. It turns out that the Kummer configuration, which appears geometrically as 16 nodes and 16 tropes of a Jacobian Kummer surface in P3, can be obtained in 24 different ways from 12 different groups. The configuration of type (A) arises in a unique way from the abelian group 8 × 2, and the one of type (B) is obtained in two ways from the groups 16Γ2b and Q8 × 2.
