You can use special PCR grade agarose. In our lab we have such agarose from old company Precision Reagents - 4.5% gel will be good. This agarose has low electroendoosmosis, i.e. LE type. LE agaroses make bands more sharper than usual type of agarose. I think there are modern analogs of such agarose, you should see in specification that EEO < 0.12 or less. The less EEO meaning the more good this agarose for your purpose.
Another solution is to make mixture gel containing some polyacrilamide. Mix gel can be handled as an agarose gel. In mix gel you definitely obtain the desired result.
First try 3% low melting (fx NuSieve) + 1% ordinary (SeaKem GTG), but it might be on the edge, with that small sizes.
Lonza got a agarose named MetaPhor agarose that they claim challenges PAGE. I´ve used it to separate bands of 660/637 on low voltage overnight, but it´s probably suitable for very small products. Do allow agarose to soak up buffer by stiring on magnetic table before cooking in microwawe.
Agarose/polyacrilamide composite gel is also called AgPAGE. In case of resolving DNA fragments use the same instruments as for standard agarose gel electrophoresis. In first place mix all components of PAGE except TEMED, then add warm agarose, mix well then add TEMED. The important moment - which temperature the agarose should have, because high temperature induces PA polymerization. If you are not intended to do gradient gel, i.e. you need just the gel, so I think you can use more hot agarose may be 40 - 50C. If you use low melting agarose you should decrease the temperature to about 32-35C. After addition of TEMED allow the gel to polymerize for about 1 hour at room temperature. May be you need optimize the concentration of the agarose and PA to obtain the better resolution. I think agarose should be at least 3.5% and PA at least 15% and may be more. In some protocols there are additional steps of treatment of the mix gel I think this is to make additional cross-links between agarose and PA