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

2026-08-23

AI Summary

该研究通过计算方法提高了51、107和115阶±1矩阵最大行列式的下界，分别改进了3.1%、0.44%和1.68%。

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.

Problem

• Hadamard Maximal Determinant Problem
• lower bounds
• determinants
• pm 1 matrices

Innovation

• Hadamard Maximal Determinant Problem
• lower bounds
• pm 1-matrices