Orthogonal arrays from Hermitian varieties

TL;DR

This paper constructs orthogonal arrays using Hermitian varieties and explores their connection to affine designs, revealing new non-classical models of affine space for q>2.

Contribution

It introduces a novel method to derive orthogonal arrays from Hermitian varieties and links these arrays to affine designs, expanding the understanding of geometric structures in combinatorics.

Findings

Orthogonal arrays constructed from Hermitian varieties.

Rows correspond to blocks of a non-classical affine design.

Provides new models of affine space for q>2.

Abstract

An orthogonal array OA(q^{2n-1},q^{2n-2}, q,2) is constructed from the action of a subset of PGL(n+1,q^2) on some non--degenerate Hermitian varieties in PG(n,q^2). It is also shown that the rows of this orthogonal array correspond to some blocks of an affine design, which for q> 2 is a non--classical model of the affine space AG(2n-1,q).