Q:

"At minimum number of simulations"

In the fragment "...to obtain optimum VTs at minimum number of simulations", should it be "a minimum", "the minimum", or is it fine as written? 
Is this similar to the case of "a number" vs. simply "number"? I prefer to keep it without an article. Please advise.

A:

The answer would depend on whether there was predefined value for "simulations". If the number of simulations is fixed then you would use "at the minimum number of simulations". However if the number of simulations is dependent upon the optimum VTs then the sentence would read "at a minimum  number of simulations".

