On n-universal quadratic forms over dyadic local fields

Let n ⩾ 2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli’s theory of bases of norm generators. Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke’s 290-theorem (or Conway and Schneeberger’s 15-theorem) on universal quadratic forms with integer coefficients.