The capabilities of the new version of the Li`ege Intra-Nuclear Cascade model (INCL++6) are presented in detail. This new version INCL is able to handle strange particles, such as kaons and the $Lambda$ particle, and the associated reactions and also allows extending nucleon-nucleon collisions up to about $15-20$ GeV incident energy. Compared to the previous version, new observables can be studied, e.g., kaon, hyperon, and hypernuclei production cross sections (with the use of a suitable de-excitation code) as well as aspects of kaon-induced spallation reactions. The main purpose of this paper is to present the specific ingredients of the new INCL version and its new features, notably the new variance reduction scheme. We also compare for some illustrative strangeness production cases calculated using this version of INCL with experimental data.
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