More generally, a smooth projective variety X over a field of characteristic p > 0 is called supersingular if all slopes of Frobenius on the crystalline cohomology Ha(X,W(k)) are equal to a/2, for all a.
For a variety X over a finite field Fq, it is equivalent to say that the eigenvalues of Frobenius on the l-adic cohomology Ha(X,Ql) are equal to qa/2 times roots of unity.
It follows that any variety in positive characteristic whose l-adic cohomology is generated by algebraic cycles is supersingular.
Conversely, the Tate conjecture would imply that every supersingular K3 surface over an algebraically closed field has Picard number 22.
Michael Artin observed that every unirational K3 surface over an algebraically closed field must have Picard number 22.
In characteristic 2, for a sufficiently general polynomial f(x, y) of degree 6, defines a surface with 21 isolated singularities.
Similarly, in characteristic 3, for a sufficiently general polynomial g(x, y) of degree 4, defines a surface with 9 isolated singularities.