  Measuring the size distribution of small (km-scale) KBOs can help constrain
models of Solar System formation and planetary migration. Such small, distant
bodies are hard to detect with current or planned telescopes, but can be
identified as sub-second occultations of background stars. We present the
analysis of data from the Weizmann Fast Astronomical Survey Telescope (W-FAST),
consisting of fast photometry of ~10^6 star hours at a frame rate of 10-25 Hz.
Our pipeline utilizes a matched-filter approach with a large template bank,
including red-noise treatment, and injection of simulated events for estimating
the detection efficiency. The KBO radius at which our survey is 10% (50%)
efficient is 1.1 (2.0) km. The data from 2020-2021 observing seasons were
analyzed and no occultations were identified. We discuss a sample of sub-second
false-positive events, both occultation-like and flare-like, which are still
not fully understood but could be instructive for future surveys looking for
short-duration events. We use our null-detection result to set limits on the
km-scale KBO number density. Our individual radius bin limits are consistent
with most previous works, with N(r>1km) <=10^6 deg^-2 (95% confidence limit).
Our integrated (all size) limits, assuming a power law normalized to large (~45
km) KBOs gives a power law index q<3.93 (95% confidence limit). Finally, our
results are in tension with a recently reported KBO detection from the ground,
at the p=4x10^-4 level.
