As Jim and others say: number-one approach - increase the diameter.
I'll add a complimentary comment. Does the section have to resist local buckling? This is a crucial issue in engineering. Sometimes with something like an aeroplane weight it crucial and you have to accept structures where if they buckle "that's it" - they are finished. For buildings and static steel structures you aften ensure that the sections will keep "distributed" bending and will never buckle.
You will have to look-up about this. For commercial steel sections it's the "Class" of a section.
-------------------------------------
That's a good point. As you increase the diameter and decrease the wall thickness of tube to increase stiffness without raising cost/weight too much the wall becomes vulnerable to indenting and buckling (sudden collapse) from concentrated stress of a load hanger, especially if it makes only point or line contact at the top. A strap reduces the concentration and a rigid pipe hanger that keeps the side walls from bulging is even better. The end supports are less of an issue because there's no bending stress there. The ends can even be flattened and drilled for a bolt.
Buckling failure is different from tension or compression failure where the metal's strength is exceeded. Buckling depends on its stiffness, resistance to bending, and becomes more likely as unsupported length increases. A wooden meter stick is easy to bend by hand though a short section of it isn't. A good example of the failure is a beer can that is very strong when filled because the internal pressure resists denting. When empty it's still fairly strong unless dented, then hand pressure can crush it flat.
Commercial tubes meant for structural strength, such as chain link fence posts, have a wall thickness around 1 to 1.5mm which resists accidental dents but allows intentional bending. I didn't mention fence posts because in the USA the commonly available ones are less than 3 meters long. Thin-walled electrical conduit is similar and sold in 10 foot lengths. Fence posts have the same outer diameter as water pipe, conduit the same inner diameter which means that their fittings and rigid hangers are different. Some combinations telescope together. Car exhaust tubing has similar walls and is sized in even fractions of an inch in the USA while water pipe, fence posts and conduit aren't, neither inch nor metric in the smaller sizes.
Yesterday I machined custom stainless flange repair fittings for exhaust tubing that measured 1.997", though it was original equipment on a vehicle made in Japan. The original (plain steel?) flange that connects the engine outlet to the converter had rusted completely off, leaving only the fillet weld which must have been stainless like the tube. I made a stainless two piece split flange that fit snugly upstream of the fillet and a solid flange to back up the graphite donut gasket below the fillet. Nuts on the spring bolts tightened the solid flange against the gasket and slightly opened the joint where the tubes contacted, allowing the springs to seal the gasket.
The exhaust leak past the unseated gasket had been very easy to find because it dripped and sprayed condensed water after a cold start. At first the gasket had appeared to seat from a tight fit on the tube but heat and pressure moved it until the tubes touched instead. I didn't know what to look for at first because I thought that area was all stainless and good for life. I had replaced the catcon only because its rear flange had rusted away enough to allow a leak.
In college while under-aged we "allowed" cider to ferment naturally.