LAUSR

We determine the indexes of all orthogonal Grassmannians of a generic 16-dimensional quadratic form in $$I^3_q$$Iq3. This is applied to show that the 3-Pfister number of the form is $$\ge $$≥4. Other consequences are: a new and characteristic-free proof of a recent result by Chernousov–Merkurjev on proper subforms in $$I^2_q$$Iq2 (originally available in characteristic 0) as well as a new and characteristic-free proof of an old result by Hoffmann–Tignol and Izhboldin–Karpenko on 14-dimensional quadratic forms in $$I^3_q$$Iq3 (originally available in characteristic $$\ne $$≠2). We also suggest an extension of the method, based on investigation of the topological filtration on the Grothendieck ring of a maximal orthogonal Grassmanian, which applies to quadratic forms of dimension higher than 16.