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As the title says, replacing k=4 by k=1 and keeping the rest of the code untouched allows the quality of the generated handwritten digits to be two or three times better.
By the way it seems that k=1 is the value used in the original paper experiments :
The number of steps to apply to the discriminator, k, is a hyperparameter. We used k = 1, the least expensive option, in our experiments.