  Using Monte Carlo simulations we study the distributions of the 3-block mass
$N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of
creating large 3-blocks in these dimensions is very small, we use a ``go with
the winners'' method of statistical enhancement to simulate configurations
having probability as small as $10^{-30}$. In earlier work, the fractal
dimensions of 3-blocks, $d_3$, in 2d and 3d were found to be $1.20\pm 0.1$ and
$1.15\pm 0.1$, respectively, consistent with the possibility that the fractal
dimension might be the same in all dimensions. We find that the fractal
dimension of 3-blocks decreases rapidly in higher dimensions, and estimate
$d_3=0.7\pm 0.2$ (4d) and $0.5\pm 0.2$ (5d). At the upper critical dimension of
percolation, $d_c=6$, our simulations are consistent with $d_3=0$ with
logarithmic corrections to power-law scaling.
