Very high specific activity (A(S)) (186g)Re could be produced by either proton or deuteron cyclotron irradiation on highly enriched (186)W target in no-carrier-added (NCA) form, leading to a A(S) very close to the theoretical carrier free (CF) value of 6.88GBqmicrog(-1). Thick target yields (TTYs), obtained irradiating both thick metal W targets of natural isotopic composition and highly enriched pressed powdered (186)W targets, were measured at different particles energies taking into account high accuracy and precision on both yield and beam energy. The measurement of radionuclidic purity of (186g)Re obtained activating highly enriched (186)W by both p and d beams were also carried out and accurately compared. The excitation function as thin-target yields (tty, i.e. proportional to the reaction cross-sections) and the integrated TTYs for all Re (A=181, 182, 183, 184, 186 and their metastable levels), W and Ta co-produced radionuclides will be presented elsewhere in deep details.