The program contains parameterizations, separately, of the total first-order 3-jet rate, the total second-order 3-jet rate, and the total 4-jet rate, all as functions of (with as a separate prefactor). These parameterizations have been obtained as follows:

- The first-order 3-jet matrix element is almost analytically integrable; some small finite pieces were obtained by a truncated series expansion of the relevant integrand.
- The GKS second-order 3-jet matrix elements were integrated for 40 different -cut values, evenly distributed in between a smallest value and the kinematical limit . For each value, 250000 phase-space points were generated, evenly in , , and the second-order 3-jet rate in the point evaluated. The properly normalized sum of weights in each of the 40 points were then fitted to a polynomial in . For the ERT(Zhu) matrix elements the parameterizations in eq. () were used to perform a corresponding Monte Carlo integration for the five values available.
- The 4-jet rate was integrated numerically, separately for and events, by generating large samples of 4-jet phase-space points within the boundary . Each point was classified according to the actual minimum between any two partons. The same events could then be used to update the summed weights for 40 different counters, corresponding to values evenly distributed in between and the kinematical limit . In fact, since the weight sums for large values only received contributions from few phase-space points, extra (smaller) subsamples of events were generated with larger cuts. The summed weights, properly normalized, were then parameterized in terms of polynomials in . Since it turned out to be difficult to obtain one single good fit over the whole range of values, different parameterizations are used above and below . As originally given, the parameterization only took into account four flavours, i.e. secondary pairs were not generated, but this has been corrected for LEP.

In the generation stage, each event is treated on its own, which means that the and values may be allowed to vary from event to event. The main steps are the following.

- 49.
- The value to be used in the current event is determined. If possible, this is the value given by you, but additional constraints exist from the validity of the parameterizations ( for GKS, for ERT(Zhu)) and an extra (user-modifiable) requirement of a minimum absolute invariant mass between jets (which translates into varying cuts due to the effects of initial-state QED radiation).
- 50.
- The value is calculated.
- 51.
- For the and values given, the relative two/three/four-jet composition is determined. This is achieved by using the parameterized functions of for 3- and 4-jet rates, multiplied by the relevant number of factors of . In ERT(Zhu), where the second-order 3-jet rate is available only at a few values, intermediate results are obtained by linear interpolation in the ratio of second-order to first-order 3-jet rates. The 3-jet and 4-jet rates are normalized to the analytically known second-order total event rate, i.e. divided by of eq. (). Finally, the 2-jet rate is obtained by conservation of total probability.
- 52.
- If the combination of and values is such that the total 3- plus 4-jet fraction is larger than unity, i.e. the remainder 2-jet fraction negative, the -cut value is raised (for that event), and the process is started over at point 3.
- 53.
- The choice is made between generating a 2-, 3- or 4-jet event, according to the relative probabilities.
- 54.
- For the generation of 4-jets, it is first necessary to make a choice between and events, according to the relative (parameterized) total cross sections. A phase-space point is then selected, and the differential cross section at this point is evaluated and compared with a parameterized maximum weight. If the phase-space point is rejected, a new one is selected, until an acceptable 4-jet event is found.
- 55.
- For 3-jets, a phase-space point is first chosen according to the
first-order cross section. For this point, the weight

is evaluated. Here is analytically given for GKS [Gut84], while it is approximated by the parameterization of eq. () for ERT(Zhu). Again, linear interpolation of has to be applied for intermediate values. The weight is compared with a maximum weight

(33) - 56.
- Massive matrix elements are not implemented for second-order QCD (but are in the first-order option). However, if a 3- or 4-jet event determined above falls outside the phase-space region allowed for massive quarks, the event is rejected and reassigned to be a 2-jet event. (The way the and variables of 4-jet events should be interpreted for massive quarks is not even unique, so some latitude has been taken here to provide a reasonable continuity from 3-jet events.) This procedure is known not to give the expected full mass suppression, but is a reasonable first approximation.
- 57.
- Finally, if the event is classified as a 2-jet event, either because it was initially so assigned, or because it failed the massive phase-space cuts for 3- and 4-jets, the generation of 2-jets is trivial.