For a high$-$performance system such as a B$-$tree index for a database, the page size is determined mainly by the data size and disk performance. Assume that on average a B$-$tree index page is $70\%$ full with fix$-$sized entries. The utility of a page is its B$-$tree depth, calculated as log$2($entries$).$ The following table shows that for $16-$byte entries, and a $10-$year$-$old disk with a $10$ ms latency and $10$ MB$/$s transfer rate, the optimal page size is $16$K$.$

$[20]<5\mathrm{.}7>$ Based on $5\mathrm{.}15\mathrm{.}2,$ what is the best page size if using a modern disk with a $3$ ms latency and $100$ MB$/$s transfer rate? Explain why future servers are likely to have larger pages.