Some Constructions of Divisible Designs from Laguerre Geometries

TL;DR

This paper presents new divisible designs constructed from finite Laguerre geometries, revealing connections to designs based on conics in projective spaces, expanding methods for combinatorial design construction.

Contribution

It introduces a novel construction of divisible designs from Laguerre geometries and links these to existing designs based on conics in projective spaces.

Findings

Constructed series of divisible designs from Laguerre geometries.

Established a connection between Laguerre-based designs and conic-based designs.

Extended the methodology for creating divisible designs in finite geometries.

Abstract

In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a 3-dimensional projective space.