We discuss how to calculate cross sections as well as rapidity, transverse momentum and energy distributions of ν τ and ν τ produced from the direct D ± s → ν τ /ν τ and chain D ±τ decays in p+ 96 Mo scattering with proton beam E lab = 400 GeV i.e. at √ s NN = 27.4 GeV. The τ decays are simulated with the help of the TAUOLA code and include multiple decay channels of τ in amounts proportional to their branching ratios. In our calculations we include D ± s from charm fragmentation c → D + s andc → D − s as well as those from subleading fragmentation of strange quarks/antiquarks s → D − s ands → D + s . The s =s asymmetry of the strange quark content of proton is included. The different contributions to D ± s and ν τ /ν τ are shown explicitly.We discuss and quantify a not discussed so far effect of asymmetries for production of ν τ and ν τ caused by subleading fragmentation mechanism and discuss related uncertainties. A potential measurement of the asymmetry is discussed. Estimates of a number of observed ν τ /ν τ in the ν τ /ν τ + 208 Pb reaction, with 2m long target are given with the help of the NuWro program. We refer also to the production of the high-energy (anti)neutrinos in the atmosphere. † also at