I have used a 6146 line amplifier tube. The coil is a 28 turns copper wire with a diameter of 2 inches and length of 3 inches. I take the feedback from the middle of the coil (at 14 turns) and the oscillator works around 5MHz. The output is a fine sinusoidal oscillation but the amplitude gradually increases upon time. I think this is attributed to over increased feedback. In transistor circuits, a one fourth feedback ratio is enough but I have no idea about that in valve based oscillators. Another possibility is the wrong matching of the oscillator that may result in returning of the output signal causing instability.
DDS modules are available at the fraction of the cost of tube.Purchase one DDS module followed by simple RF amplifier..With in 15$ you can complete the project.