New symmetric 2-(176,50,14) designs

TL;DR

This paper constructs two new symmetric 2-(176,50,14) designs invariant under specific automorphism subgroups, one self-dual with a large automorphism group, and the other non-self-dual with a smaller automorphism group.

Contribution

The paper introduces two novel symmetric designs with specified parameters, expanding the catalog of known combinatorial designs and automorphism group structures.

Findings

One design is self-dual with automorphism group size 11520.

The other design is non-self-dual with automorphism group size 2520.

Both designs are invariant under certain subgroups of the Higman design's automorphism group.

Abstract

In this paper we construct two new symmetric designs with parameters 2-(176,50,14) as designs invariant under certain subgroups of the full automorphism group of the Higman design. One is self-dual and has the full automorphism group of size 11520 and other is not self-dual and has the full automorphism group of size 2520.