Fluxgate sensors with straight wire or rod cores are used in nondestructive testing (NDT), portable gradiometers, and sensor arrays and for the detection of small objects. We show that their sensitivity at the voltage output mode depends on the excitation parameters, properties of the core material and geometry, pick-up coil length, but only slightly on the pick-up coil diameter. This finding allows one to design multiwire cores with large wire pitch, which decreases their magnetic interactions and thus reduces demagnetization and correlation of their noise. As a result, using <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> wires theoretically increases sensitivity <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-times, which is not achievable with dense cores. We have demonstrated this tendency for <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> up to 8 and one type of permalloy wire.