High-time-resolution counters based on plastic scintillator with silicon photomultiplier (SiPM) readout have been developed for applications to high energy physics experiments for which relatively large-sized counters are required. We have studied counter sizes up to $120times40times5$ mm^3 with series connection of multiple SiPMs to increase the sensitive area and thus achieve better time resolution. A readout scheme with analog shaping and digital waveform analysis is optimized to achieve the highest time resolution. The timing performance is measured using electrons from a Sr-90 radioactive source, comparing different scintillators, counter dimensions, and types of near-ultraviolet sensitive SiPMs. As a result, a resolution of $sigma =42 pm 2$ ps at 1 MeV energy deposition is obtained for counter size $60times 30 times 5$ mm^3 with three SiPMs ($3times3$ mm^2 each) at each end of the scintillator. The time resolution improves with the number of photons detected by the SiPMs. The SiPMs from Hamamatsu Photonics give the best time resolution because of their high photon detection efficiency in the near-ultraviolet region. Further improvement is possible by increasing the number of SiPMs attached to the scintillator.
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