You might want to check out Polya's Theorem. It may or may not be worth your time. The gist of Polya's theorem is the enumeration of things under rotations and flips. For instance, let's take a 3x3 board and place an L-shaped triomino on it. The following are considered equivilant:

...
x..
xx.

...
..x
.xx

xx.
x..
...

.xx
..x
...
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because any one can be obtained from any other by a rotation of the board. This should drastically cut down on the number of boards that you have deal with. Then again, it may not. I haven't used this in years, and it may only be good for counting such things, though my memory tells me otherwise.

thor