Locally resolvable BIBDs and generalized quadrangles with ovoids

TL;DR

This paper establishes a correspondence between generalized quadrangles with ovoids and certain BIBDs with local resolution systems, providing new insights into their structural relationships and constructions.

Contribution

It introduces a novel correspondence linking generalized quadrangles with ovoids to BIBDs with non-triangular local resolution systems, expanding understanding of their combinatorial structures.

Findings

Established a 1-to-1 correspondence between generalized quadrangles with ovoids and specific BIBDs.

Presented a non-triangular local resolution system for a BIBD construction.

Connected difference family BIBDs to generalized quadrangles with ovoids.

Abstract

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.