On the Length of a Hilbert Ascending Chain

It is shown that if a bound $f(i)$ is placed on the degrees of the elements in some basis of an ideal Aᵢ in the polynomial ring k[X₁, ⋯ ,Xₙ] over the field k,i = 0,1,2, ⋯, then a bound can be placed on the length of a strictly ascending chain A₀ < A₁ < ⋯. Moreover one could explicitly write down a formula for a bound gₙ in terms of f and n.