Maximal (120,8)-arcs in projective planes of order 16 and related designs

TL;DR

This paper computes all maximal sets of compatible resolutions for certain 2-(120,8,1) designs derived from maximal (120,8)-arcs in projective planes of order 16, showing each design's unique embeddability.

Contribution

It provides a complete classification of resolutions and embeddings of these designs, revealing their unique embedding properties in the projective plane of order 16.

Findings

All resolutions are computed and classified.

Each design embeds uniquely in the projective plane of order 16.

The structure of maximal (120,8)-arcs and related designs is fully characterized.

Abstract

The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising frommaximal (120,8)-arcs in the known projective planes of order 16 are computed. It is shown that each of these designs is embeddable in a unique way in a projective plane of order 16.