We use the known values of the two-loop Wilson coefficients and the three-l
oop anomalous dimension matrix gamma(n) to perform a next-to-next-to leadin
g order (NNLO) calculation of ep deep inelastic scattering. Because gamma(n
) is only known for a few values of n, the method of average reconstruction
has to be used, which leaves 102 effective experimental points, for 12 par
ameters: the QCD mass Lambda, and 11 initial values for the moments of the
structure functions. The data points spread in the range of momenta 2.5 GeV
2 less than or equal to Q(2) less than or equal to 230 GeV2. The chi(2)/d.o
.f. decreases substantially when going from LO to NLO, and also from NLO to
NNLO (although only a little now) to chi(2)/d.o.f. = 79.2/(102 - 12). The
favoured value of Lambda is Lambda(n(f) = 4,3 loop) = 282.7 +/- 35.1 MeV, c
orresponding to the value of the coupling at the Z mass of alpha(s)(( 3 loo
p))(M-Z(2)) = 0.1172 +/- 0.0024. The calculation, which constitutes a very
precise test of QCD, includes target mass corrections; the error takes into
account experimental errors and higher twist effects among other estimated
theoretical errors. (C) 1999 Elsevier Science B.V. All rights reserved.