Every maximally nodal sextic surface contains a symmetric half-even set of 35 nodes, so its equation is the determinant of a symmetric 6x6 matrix of linear forms.
Kurz, Codes of Nodal Sextics with Many Nodes , in Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces , Lect
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Maximally nodal sextic surfaces and linear determinantal representations
Every maximally nodal sextic surface contains a symmetric half-even set of 35 nodes, so its equation is the determinant of a symmetric 6x6 matrix of linear forms.