arXiv:2611.07171v1 Announce Type: new Abstract: Multiuser networks can aggregate local observations through a shared receiver. In this paper, we study the particle budget required to recover the exact sum of binary inputs in a multiuser network. We show that, for the considered model, the minimum budget grows quadratically with the number of transmitters when the symbol duration and target error probability are fixed, even when the receiver observes all particle arrival times. Simultaneous on-off keying (OOK) achieves this quadratic scaling, while any slower budget growth makes the error probability approach one at a fixed symbol duration, regardless of the transmission and decoding scheme. We then examine how this particle requirement can be reduced by allowing longer symbol durations and more counting intervals. We develop a groupwise OOK counting (GOC) scheme with staggered group releases and sequential estimation of group input sums, accounting for delayed arrivals. Our bounds show that, when reception is based on interval counts, reducing the quadratic scaling requires both the symbol duration and the number of counting intervals to grow with network size. When both grow in proportion to network size, the minimum budget becomes proportional to the number of transmitters times its logarithm.