CCDN Proposition 5 with its exact constant 1/5, for an absolutely irreducible projective plane equation. The principal ideal is prime and its projective Hilbert degree is the prescribed degree.

theorem CCDN.projective_integral_curve_lower_bound (d : ℕ) (hd : 0 < d) : ∃ (F : MvPolynomial (Fin 3) ℚ) (B : ℕ), 1 ≤ B ∧ F.IsHomogeneous d ∧ F.totalDegree = d ∧ AbsolutelyIrreducibleRat F ∧ (Ideal.span {F}).IsPrime ∧ HasProjectiveCurveDegree (Ideal.span {F}) d ∧ ↑d ^ 2 / 5 * ↑B ^ (2 / ↑d) ≤ ↑(projectiveCount (projectiveIdealZeroLocus (Ideal.span {F})) ↑B)

The lower-bound equation defines an integral homogeneous plane curve whose degree is also certified by the projective Hilbert function.