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The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale Lambda = 1.1 x 10(17) GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value m(H) = 175.1(-9.8)(+5.8) GeV obtained from noncommutative geometry for the standard model with three generations only. (c) 2006 Published by Elsevier B.V .