The total number of Slater determinants which can be built with say \( N \) neutrons distributed among \( n \) single particle states is $$ \left (\begin{array}{c} n \\ N\end{array} \right) =\frac{n!}{(n-N)!N!}. $$
For a model space which comprises the first for major shells only \( 0s \), \( 0p \), \( 1s0d \) and \( 1p0f \) we have \( 40 \) single particle states for neutrons and protons. For the eight neutrons of oxygen-16 we would then have $$ \left (\begin{array}{c} 40 \\ 8\end{array} \right) =\frac{40!}{(32)!8!}\sim 10^{9}, $$ and multiplying this with the number of proton Slater determinants we end up with approximately witha dimensionality \( d \) of \( d\sim 10^{18} \).