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Recently it has been shown that four constant memory, deterministic agentsare able to discover the integer lattice if only local, constant-sizecommunication is allowed. Moreover, if the agents' choices are determined withthe help of a fair coin, it has been shown that three are necessary andsufficient to discover the integer lattice. In this paper, we show that threedeterministic agents cannot find the integer lattice and sketch a possiblecharacterization for one explorer, three beacons type of exploration algorithm.

On deterministic, constant memory triangular searches on the integer lattice