The spectrum for large sets of $(3,\lambda)$-GDDs of type $g^u$

TL;DR

This paper completely characterizes the existence conditions for large sets and simple instances of (3,λ)-group divisible designs of type g^u, advancing combinatorial design theory.

Contribution

It provides a complete solution to the existence problem for large sets and simple (3,λ)-GDDs of type g^u, which was previously unresolved.

Findings

Complete existence characterization for large sets of (3,λ)-GDDs.

Existence criteria for simple (3,λ)-GDDs of type g^u.

Advancement in combinatorial design theory.

Abstract

In this paper, we completely solve the existence of large sets of $(3,\lambda)$-GDDs of type $g^u$ and the existence of a simple $(3,\lambda)$-GDD of type $g^u$.