  The network slice management function (NSMF) in 5G has a task to configure
the network slice instances and to combine network slice subnet instances from
the new-generation radio access network and the core network into an end-to-end
network slice instance. In this paper, we propose a mathematical model for
network slicing based on combinatorial designs such as Latin squares and
rectangles and their conjugate forms. We extend those designs with attributes
that offer different levels of abstraction. For one set of attributes we prove
a stability Lemma for the necessary conditions to reach a stationary ergodic
stage. We also introduce a definition of utilization ratio function and offer
an algorithm for its maximization. Moreover, we provide algorithms that
simulate the work of NSMF with randomized or optimized strategies, and we
report the results of our implementation, experiments and simulations for one
set of attributes.
