First of all - a number must not occur twice, that is implied since we're talking about permutations. So filling the table with a simple random(255) function won't work.

Secondly, you need to ensure that there are no premature recurrence patterns:

Consider the values 1,2,3,4 - the permutation table 4,3,2,1 is not a very good one because recurrence happens immediately, i.e. 1 -> 4, 4 -> 1. Likewise with 4,2,3,1 or 1,2,3,4. The optimal tables take you all the way through all positions: 3,1,4,2 or 2,4,1,3.

This property becomes increasingly important as you increase the number of dimensions and perform recursive lookups.

Thirdly, For larger tables like one with 256 values you need to ensure a uniform random distribution, so you may want to constrain the random step distance to a certain min and max range, e.g. 5..120 or something. These numbers are worth experimenting with.

First of all - a number must not occur twice, that is implied since we're talking about permutations. So filling the table with a simple random(255) function won't work.

Secondly, you need to ensure that there are no premature recurrence patterns:

Consider the values 1,2,3,4 - the permutation table 4,3,2,1 is not a very good one because of its short cyclic properties, i.e. 1 -> 4, 4 -> 1. Likewise with 4,2,3,1 or 1,2,3,4. The optimal tables take you all the way through all positions: 3,1,4,2 or 2,4,1,3.

This property becomes increasingly important as you increase the number of dimensions and perform recursive lookups.

However this approach alone may create clusters of too similar values, which may or may not be wanted, which leads me to next point.

Thirdly, When you generate a table with the non cyclic properties, you need to step through remaining unassigned indices in a random manner. When possible constrain the random step distance here to a certain min and max range, e.g. 5..120 to avoid clustered groups of similar values. These numbers are worth experimenting with.