It wasn't mentioned if this antenna is to be used for receiving, transmitting or both.
For a receive only antenna, try an active antenna. The element doesn't need to be at a resonant length for any of the frequencies desired, in fact, it really shouldn't be resonant at any of the frequencies desired.
You will need to design a broad band LNA, I doubt if a MMIC will have a low enough noise figure for your purposes.
For transmit or transceive operations, it becomes a stickier situation, You might be able to design a conical monopole, biconical or discone with that kind of bandwidth, however there will be other problems such as beam tilt and group delay at certain frequencies.
A 17-element LPDA (Log Periodic Dipole Array) could be etched on a piece of double sided Printed circuit board which would cover that frequency range, however it would be directional and have around a 7 dBi gain. Try a Tau of .8 and a Sigma of .21. Be aware that the longest element will be 375 mm and the length of the array will be about 859 mm depending upon how you terminate or connectorize the antenna, so you will need a really BIG piece of double- side PCB.
I remain,
The Old Soldering Gunslinger