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In this paper, we improve the lower bound on the maximum nonlinearity of 1resilient Boolean functions, for n even, by proposing a method of constructing this class of functions attaining the best nonlinearity currently known. Thus for the first time, at least for small values of n, the upper bound on nonlinearity can be reached in a deterministic manner in difference to some heuristic search methods proposed previously. The nonlinearity of these functions is extremely close to the maximumdoi:10.1016/j.ins.2016.10.001 fatcat:xttyrajfkzb2tg2xwibzkrq45e