Linked systems of symmetric group divisible designs of type II

TL;DR

This paper introduces linked systems of symmetric group divisible designs of type II, explores their construction from affine resolvable designs and Latin squares, and establishes their equivalence with certain 5-class association schemes.

Contribution

It presents the concept of linked systems of symmetric group divisible designs of type II and links them to association schemes, expanding the theoretical framework.

Findings

Examples derived from affine resolvable designs and Latin squares

Establishment of equivalence with 5-class association schemes

New insights into the structure of symmetric group divisible designs

Abstract

The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group divisible designs and some association schemes with $5$-classes is provided.