A nanosecond is one-billionth of a second, but time can be measured by increments far shorter. A picosecond is three orders of magnitude shorter, one-trillionth of a second, and a femtosecond is shorter still at one-quadrillionth of a second.
Dividing the second still further, and by three orders of magnitude each time, the divisions are attoseconds, zeptoseconds and yoctoseconds; the last of these is 0.000,000,000,000,000,000,000,001 second. According to Wikipedia, the shortest theoretical increment of time is the Planck time. This is the time taken for a photon, traveling at the speed of light, to cross a Planck distance. This upper limit is 10^-43 second.