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

翻译：最近的研究表明，如果只允许局部、固定大小的通信，四个具有恒定内存的确定性探测器能够发现整数格。此外，如果代理的选择是在公平硬币的帮助下确定的，则已经证明三个探测器是必要的并足够发现整数格。在本文中，我们展示了三个确定性探测器无法找到整数格，并概述了一种可能的一个探测器和三个信标的类型探测算法的特征。