Sets of mutually orthogoval projective and affine planes

TL;DR

This paper introduces new constructions for sets of mutually orthogoval projective and affine planes, explores their properties, and discusses their connection to covering arrays, expanding understanding of these geometric structures.

Contribution

It provides novel methods to construct mutually orthogoval planes and reviews existing results, linking these structures to covering arrays.

Findings

New constructions for mutually orthogoval planes

Review of known results on orthogoval plane sets

Discussion of the connection to covering arrays

Abstract

A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions for sets of mutually orthogoval planes, both projective and affine, and review known results that are equivalent to sets of more than two mutually orthogoval planes. We also discuss the connection between sets of mutually orthogoval planes and covering arrays.