# Taming the Differences: Exploring Paradigm Shifts in the Construction of Difference Sets

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Delaware (DE) · $203,650

## Abstract

In this information-driven world, discrete mathematics forms the backbone of many essential technologies and systems. At the heart of this field are objects with strong regularity, which are central to the branch of mathematics known as combinatorics. The current project studies difference sets and partial difference sets, both of which can be neatly described as subsets exhibiting remarkable regularity. These are the underlying objects behind many elegant configurations in a wide range of areas including, on the theory side: finite geometry, coding theory, combinatorial design theory, number theory, graph theory, and on the application side: sequence design, signal processing, information security. Despite their wide-reaching significance, finding explicit constructions of these sets has remained a long-standing challenge. This project embraces an ongoing paradigm shift in the approach to constructing such objects, with the goal of uncovering novel constructions that will substantially advance the constructive landscape of difference sets and partial difference sets. The PI plans to involve graduate students.


This project investigates the central challenge in the study of difference sets and partial difference sets: their explicit constructions. Inspired by the recent breakthrough of Applebaum et al., which determined exactly which of the 56,092 non-isomorphic groups of order 256 contain a difference set, the project will pursue three key directions: (1) constructing di

## Key facts

- **NSF award ID:** 2452236
- **Awardee organization:** University of Delaware (DE)
- **SAM.gov UEI:** T72NHKM259N3
- **PI:** Shuxing Li
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** EXP PROG TO STIM COMP RES
- **Estimated total:** $203,650
- **Funds obligated:** $203,650
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2452236

## Citation

> US National Science Foundation, Award 2452236, Taming the Differences: Exploring Paradigm Shifts in the Construction of Difference Sets. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2452236. Licensed CC0.

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