We provide explicit descriptions of the generic members of Hassett's divisors
Cdβ for relevant 18β€dβ€38 and for d=44. In doing so, we
prove that Cdβ is unirational for 18β€dβ€38,d=44. As a
corollary, we prove that the moduli space Ndβ of polarized K3
surfaces of degree d is unirational for d=14,26,38. The case d=26 is
entirely new, while the other two cases have been previously proven by Mukai.Comment: 13 pages, 2 tables. Script for the computer calculations used are
provided on the author's websit