How to do exhaustive search in case of Maximum Likelihood detector in MATLAB ?

Hello all, I came across the following Maximum Likelihood detector expression:

----(1)

where is received signal of dimension , is channel between transmitter to receiver of dimension and is transmitted signal of dimension such that , L denotes time slots. is a set that consists of N column vectors of dimension .

Also each , i ranging from 1 to L, is chosen randomly from set .

My query is how to do exhaustive search over .

Any help in this regard will be highly appreciated.