  The binary perceptron is the simplest artificial neural network formed by $N$
input units and one output unit, with the neural states and the synaptic
weights all restricted to $\pm 1$ values. The task in the teacher--student
scenario is to infer the hidden weight vector by training on a set of labeled
patterns. Previous efforts on the passive learning mode have shown that
learning from independent random patterns is quite inefficient. Here we
consider the active online learning mode in which the student designs every new
Ising training pattern. We demonstrate that it is mathematically possible to
achieve perfect (error-free) inference using only $N$ designed training
patterns, but this is computationally unfeasible for large systems. We then
investigate two Bayesian statistical designing protocols, which require $2.3 N$
and $1.9 N$ training patterns, respectively, to achieve error-free inference.
If the training patterns are instead designed through deductive reasoning,
perfect inference is achieved using $N\!+\!\log_{2}\!N$ samples. The
performance gap between Bayesian and deductive designing strategies may be
shortened in future work by taking into account the possibility of ergodicity
breaking in the version space of the binary perceptron.
