Let $${\mathcal {F}}$$F be a set of functions of $$f : X \rightarrow Y$$f:X?Y, where $$|X|=k, \,|Y|=v$$|X|=k,|Y|=v and $$|{\mathcal {F}}|=N$$|F|=N. If for any $$t$$t-subset $$C \subseteq X$$C⊆X there exists at least one function $$f\in \mathcal {F}$$f?F such that $$f|_{C}$$f|C is one-to-one, then $${\mathcal {F}}$$F is called a perfect hash family, denoted by PHF$$(N; k, v, t)$$(N?k,v,t). In this paper, we construct the simplest nontrivial PHFs of $$t=3$$t=3 and $$N=3$$N=3 using classic generalized quadrangles, quadrics in PG$$(4, q)$$(4,q) and Hermitian varieties in PG$$(4, q^2)$$(4,q2). We obtained PHF$$(3; q^2(q+1), q^2, 3)$$(3?q2(q+1),q2,3) and PHF$$(3; q^5, q^3, 3)$$(3?q5,q3,3) for $$q$$q a prime power. The curve $$k= v^{5/3}$$k=v5/3 is greater than known $$k$$k for $$v=q^3,\,q$$v=q3,q a prime power.