How to use a higher precision?

Question

Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$?

n = 15;
roots = Table[Sqrt[Prime[i]], {i, n}];
W = 10^45;
A = Table[0, {i, 1,  n + 1}, {j, 1, n + 1}];
A[[1, 1]] = 1; 
For[i = 1, i <= n, i++, A[[1, i + 1]] = Round[W*roots[[i]]];];
For[i = 2, i <= n + 1, i++, A[[i, i]] = W; ];
b = LatticeReduce[A];
q = Abs[b[[1, 1]]]

The error message is here:

N::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating -28254824730949473896127703534134355343731647793777+19979178168491741166272766531031078657045486457686 Sqrt[2].

My version is V9, and my OS is windows 7.

Answer 1

This appears to work without error in v10.1 under Windows x64:

n = 15;
roots = Table[Sqrt[Prime[i]], {i, n}];
W = 10^200;
A = Table[0, {i, 1, n + 1}, {j, 1, n + 1}];
A[[1, 1]] = 1;
For[i = 1, i <= n, i++, A[[1, i + 1]] = Round[W*roots[[i]]];];
For[i = 2, i <= n + 1, i++, A[[i, i]] = W;];
b = LatticeReduce[A];
q = Abs[b[[1, 1]]]

485603484508849372516130007418504632602233691958877412852766931375138423098986536885\
657362770183762005362519092758826679723076465340151346365557521902058790127411374224\
440956272176411511