New Records for the Hadamard Maximal Determinant Problem in Dimensions $51$, $107$, and $115$

We compute new lower bounds for determinants of $\{\pm 1\}$-matrices of orders $n=51$, $n=107$ and $n=115$, improving previous recorded bounds by $3.1\%$, $0.44\%$, and $1.68\%$, respectively. We provide the data necessary to construct these matrices.

Authors

Sergei Gukov (ORCID: https://orcid.org/0000-0002-9486-1762)
Justin Tan (ORCID: https://orcid.org/0009-0008-2344-6992)
Pragatheeswaran Vipulanandan
Giorgi Butbaia
Xiaoyu Huang
Lucas Fagan
Toby Saunders-A'Court
Davide Passaro
Michele Tarquini

Institutions

California Institute of Technology (US)
University of Miami (US)
University of Cambridge (GB)
Temple College (US)
Temple University (US)

Publication Details

Journal: Zenodo (CERN European Organization for Nuclear Research)
Published: 2026-08-20
DOI: https://doi.org/10.5281/zenodo.22024186
Primary Topic: graph theory and CDMA systems
Type: preprint

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preprint

New Records for the Hadamard Maximal Determinant Problem in Dimensions $51$, $107$, and $115$

Sergei Gukov, Justin Tan, Pragatheeswaran Vipulanandan, Giorgi Butbaia et al.

Aug 20, 2026

Zenodo (CERN European Organization for Nuclear Research)

graph theory and CDMA systems

preprint

New Records for the Hadamard Maximal Determinant Problem in Dimensions $51$, $107$, and $115$

Sergei Gukov, Justin Tan, Pragatheeswaran Vipulanandan, Giorgi Butbaia, Xiaoyu Huang, Lucas Fagan, Toby Saunders-A'Court, Davide Passaro, Michele Tarquini

August 20, 2026preprint en

Abstract

We compute new lower bounds for determinants of $\{\pm 1\}$-matrices of orders $n=51$, $n=107$ and $n=115$, improving previous recorded bounds by $3.1\%$, $0.44\%$, and $1.68\%$, respectively. We provide the data necessary to construct these matrices.

Zenodo (CERN European Organization for Nuclear Research)

California Institute of Technology (US), University of Miami (US), University of Cambridge (GB), Temple College (US), Temple University (US)

graph theory and CDMA systems

DOI Open Access PDF OpenAlex

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New Records for the Hadamard Maximal Determinant Problem in Dimensions $51$, $107$, and $115$ — Sergei Gukov, Justin Tan, et al. · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS