Determine whether five mutually unbiased weighing matrices exist at order 20

Determine whether a set of five mutually unbiased weighing matrices of order 20 and weight 9 exists.

Background

The construction in the paper establishes a set of four mutually unbiased weighing matrices of order 20 and weight 9. The authors then search for a fifth matrix compatible with such a set, but the search does not resolve whether five mutually unbiased weighing matrices exist. The general upper bound obtained in the paper is 34, leaving a substantial gap between the known construction and the upper bound.