Glass tube element with improved quality

A glass tube element, comprising:

• a hollow cylindrical section having a shell, a sub-section, and a main extension along a center axis, wherein the shell has an outer diameter in a specific cross-sectional plane that is perpendicular to the main extension, wherein the outer diameter in the specific cross-sectional plane has a minimal outer diameter and a maximal outer diameter, wherein the sub-section has a start, an end, and a distance measured along a straight line from the start to the end and intersecting with the center axis 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 first ratio that is smaller than 0.005, the first ratio being of an absolute value to a mean value, the absolute value being a difference of the minimal and the maximal outer diameters, and the mean value being of the minimal and maximal outer diameters;
• and
• a second ratio that is smaller than 0.00075, the second ratio being of a specific distance to 1 meter, the specific distance being defined as a largest of all shortest distances.