Shrinking an Interval by a Factor of 2.8

A quality engineer measures a random sample of $n = 100$ parts and reports a 95% confidence interval for the population mean of the form

$\bar{x} \pm z^{*}\frac{\sigma}{\sqrt{n}}, \qquad z^{*} = 1.96$

Her reported margin of error is $0.784$ mm. The population standard deviation $\sigma$ is known and will not change.

She now needs the margin of error to be at most $0.28$ mm, still at 95% confidence.

What is the smallest sample size that achieves this?