The cubic minimally nonideal matrix order conjecture

A cubic minimally nonideal matrix is a minimally nonideal matrix whose Lehman core is cubic, and an $n\times n$ matrix is square with $n$ rows and $n$ columns. Cubic mni order conjecture. There are no $n\times n$ cubic minimally nonideal matrices for $n>17$. The conjecture is motivated by the paper's computational enumeration, which finds only small cubic Lehman graphs that are minimally nonideal; whether larger square cubic minimally nonideal matrices exist remains open.