Tiling with triominoes

[Susam Pal]

There is a square board made of at least 4 equal-sized squares. The
number of squares in the board is a power of 2. An unlimited number of
L-shaped triominoes are given. Each triomino is made of 3 equal-sized
squares. Each equal-sized square that makes a triomino has the same
dimensions as that of each equal-sized square that makes the square
board.

The square board needs to be tiled with the L-shaped triominoes such
that each square is covered at most once without parts of each
triomino extending beyond the 3 squares it covers.

What is the minimum number of squares that can't be covered with the
triominoes?

http://cotpi.com/p/20/