Enumerations of 1-rotational Steiner systems

TL;DR

This paper introduces new 1-rotational 2-Steiner systems for various parameters and enumerates 1-rotational unitals of order 4, expanding the understanding of these combinatorial designs.

Contribution

It provides the first enumeration of 1-rotational unitals of order 4 and constructs new 1-rotational 2-Steiner systems for different admissible pairs.

Findings

New 1-rotational 2-Steiner systems for various v,k pairs

Enumeration of 1-rotational unitals of order 4

Expanded catalog of 1-rotational combinatorial designs

Abstract

In this paper new $1$-rotational 2-Steiner systems for different admissible $v,k$ pairs are introduced. In particular, $1$-rotational unitals of order $4$ are enumerated.