This work studies the fundamental search problem of\textsc{element-extraction} in a query model that combines both: linearmeasurements with bounded adaptivity . In the problem, one is given a nonzero vector$\mathbf{z} = (z_1,\ldots,z_n) and must report an index$i$where$z_i = 1$. This problem admits an efficient nonadaptiverandomized solution (through the well known technique of$ell_0$-sampling) and an efficient fully adaptive deterministic solution . Weprove that when confined to only$k$rounds of adaptivity, a deterministic . algorithm must spend$Omega(k (n = 1/k)$queries, when working in the ring of integers modulo some fixed$q$. Thismatches the corresponding upper bound. For queries using integer arithmetic, weprove a$2\$-round

Author(s) : Amit Chakrabarti, Manuel Stoeckl