  Due to some significantly contradicting research results, we reconsider the
problem of the online exploration of a simple grid cell environment. In this
model an agent attains local information about the direct four-neigbourship of
a current grid cell and can also successively build a map of all detected
cells. Beginning from a starting cell at the boundary of the environment, the
agent has to visit any cell of the grid environment and finally has to return
to its starting position. The performance of an online strategy is given by
competitive analysis. We compare the number of overall cell visits (number of
steps) of an online strategy to the number of such visits in the optimal
offline solution under full information of the environment in advance. The
corresponding worst-case ratio gives the competitive ratio. The aforementioned
contradiction among two publications turns out to be as follows: There is a
journal publication that claims to present an optimal competitive strategy with
ratio 7/6 and a former conference paper that presents a lower bound of 20/17.
In this note we extract the flaw in the upper bound and also present a new
slightly improved and (as we think) simplified general lower bound of 13/11.
