Glass tube element with improved quality

A glass tube element having a hollow cylindrical section with a shell having an outer diameter is provided. A first ratio is a difference value to a mean value. The difference value is a difference of a minimal and maximal value of the outer diameter. The mean value is a mean of the minimal and maximal values. A sub-section having a start, an end, and a distance of 1 meter measured along a straight line from the start to the end and intersecting with a center axis of the sub-section at the start and the end. The sub-section having, for every point of the center axis, a shortest distance to the straight line. A second ratio of a specific distance to 1 meter, the specific distance being defined as a largest of all shortest distances. A product of the first and second ratio is smaller than 4×10−6.