I am a mathematician and this is my first time using Stack Overflow, sorry if the question is not adequate or there is some better place to ask this. I would like to know if there is a standard way to do the following. Let $d$ be some small distance (e.g. $d=0.03$).

I want to create in Python a list $L$ of points of the sphere $mathbb{S}^4$, so each point is a vector like $[0.5,0.5,0.5,0.5,0]$, such that every point of $mathbb{S}^4$ is at distance $<d$ of some point of $L$. I also need the list to not be very long, it should not have more than $10^8$ points (I guess that means that I cannot expect this to work for $d<0.02$ aprox).

The most important thing is that we are absolutely sure that any point of $mathbb{S}^4$ is at distance $<d$ of some point of $L$, as I plan to use this list in a mathematical proof if it ends up being feasible. I have seen other questions but they either did not adress this point or they are for the $2$-dimensional sphere $mathbb{S}^2$.

I have some ideas for how to create the list (e.g. take evenly spaced points in the boundary of the cube $[-1,1]^5$ and then project them to $mathbb{S}^4$) but they seem like they would be pretty inefficient and I would end up with at least twice as many points as necessary so I will not get a value of $d$ as small as possible. Maybe some approach based on triangulating the sphere could be more efficient, but I am not sure how to implement that. To sum up, I just want to know if someone has already optimized this process.