Almost tight bounds for $\epsilon$-nets

Given any natural numberd, 0<d - 2 + \frac2d + 2 \leqslant lime® 0 \fracfd (e)(1/e)log(1/e) \leqslant d.Unknown control sequence '\leqslant' Further, we prove thatf 1()=max(2, 1/ –1), and similar bounds are established for some special classes of range spaces of Vapnik-Chervonenkis dimension three.