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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 ofcreating large 3-blocks in these dimensions is very small, we use a ``go withthe winners'' method of statistical enhancement to simulate configurationshaving probability as small as $10^{-30}$. In earlier work, the fractaldimensions 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 fractaldimension might be the same in all dimensions. We find that the fractaldimension 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 ofpercolation, $d_c=6$, our simulations are consistent with $d_3=0$ withlogarithmic corrections to power-law scaling.Comment: figures best viewed when printe

Fractal dimension of 3-blocks in four-, five-, and six-dimensional percolation systems