$SU(2)$ has a nice parametrzed representation which allows me to iterate over the parameters and generate the matrices. Is there anything similar for $SU(4)$? I came across the generators but not sure as to how to use them to generate matrices that span the entitre space of $U(4)$. Ref : http://www.ejtp.com/articles/ejtpv10i28p9.pdf
I also came across a mathematica code that does generate random matrices but I am looking for a methodical iterative way to go about it similar to $SU(2)$. Ref : https://www.google.co.in/url?cad=rja&cd=1&esrc=s&q=&rct=j&sa=t&sig2=s_Df5GaAh0Uxh5dSQegW9Q&source=web&uact=8&url=http%3A%2F%2Fhome.lu.lv%2F%7Esd20008%2Fpapers%2Fessays%2FRandom%2520unitary%2520%5Bpaper%5D.pdf&usg=AFQjCNHhDcOWxktNNYeJsAYEIIW7g4l0NA&ved=0ahUKEwjUzqOVtKHUAhXLPo8KHR6aDr8QFggnMAA
PS : I do not understand Lie groups and just looking for a method to iterate over the space of $U(4)$ efficiently.