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The Merian survey is mapping ∼ 850 deg2 of the Hyper Suprime-Cam Strategic Survey Program (HSC-SSP) wide layer with two medium-band filters on the 4-m Victor M. Blanco telescope at the Cerro Tololo Inter-American Observatory, with the goal of carrying the first high signal-to-noise (S/N) measurements of weak gravitational lensing around dwarf galaxies. This paper presents the design of the Merian filter set: N708 (λ c  = 7080 Å, Δλ = 275 Å) and N540 (λ c  = 5400 Å, Δλ = 210 Å). The central wavelengths and filter widths of N708 and N540 were designed to detect the |$\rm H\alpha$| and |$\rm [OIII]$| emission lines of galaxies in the mass range |$8\lt \rm \log M_*/M_\odot \lt 9$| by comparing Merian fluxes with HSC broad-band fluxes. Our filter design takes into account the weak lensing S/N and photometric redshift performance. Our simulations predict that Merian will yield a sample of ∼ 85 000 star-forming dwarf galaxies with a photometric redshift accuracy of σΔ z /(1 + z) ∼ 0.01 and an outlier fraction of |$\eta =2.8~{{\ \rm per\ cent}}$| over the redshift range 0.058 < z < 0.10. With 60 full nights on the Blanco/Dark Energy Camera (DECam), the Merian survey is predicted to measure the average weak lensing profile around dwarf galaxies with lensing S/N ∼32 within r < 0.5 Mpc and lensing S/N ∼90 within r < 1.0 Mpc. This unprecedented sample of star-forming dwarf galaxies will allow for studies of the interplay between dark matter and stellar feedback and their roles in the evolution of dwarf galaxies. [ABSTRACT FROM AUTHOR]