The equivalence of two inequalities for quasisymmetric designs

TL;DR

This paper demonstrates that Hobart's inequality for quasisymmetric 2-designs is equivalent to known inequalities by Neumaier and Calderbank, clarifying their relationship and providing new parameter restrictions.

Contribution

It establishes the equivalence between Hobart's inequality and earlier inequalities, and extends parameter restrictions using the Blokhuis-Calderbank inequality.

Findings

Hobart's inequality is equivalent to Neumaier and Calderbank's inequalities.

New parameter sets are ruled out by the Blokhuis-Calderbank inequality.

Clarifies the relationship among key inequalities in quasisymmetric 2-designs.

Abstract

It has been an open problem whether Hobart's inequality on the parameters of a quasisymmetric 2-design is independent of earlier known restrictions. In this note we show that it is equivalent to inequalities found by Neumaier and Calderbank. We also give some more parameter sets ruled out by the Blokhuis-Calderbank inequality.