Algorithmizing Aspects of Some Combinatorial Block-Designs Implemented in Network Systems

The main numerical characteristics of a number of combinatorial block designs (CBD), which are essential for choosing parameters of network systems of combinatorial block structure are given. In addition to the traditionally considered blocks of CBD, attention is paid to dual blocks, formed by combinations of blocks containing a certain element. By combining blocks and dual blocks in one block design the so-called combined CBD is generated, the elements of which are pairs (block, element of this block). This achieves the scaling effect of the network system. The stage of its synthesis consists in the selection of CBD in accordance with the requirements of the parameters of the network system and its subsystems, as well as the links between subsystems. The main result are sets of algorithms for computing blocks, dual blocks as well as intersections of two blocks and two dual blocks for systems of Steiner triples, projective and affine geometries and transversal combinatorial block-designs. They are used to derive algorithms for computing lists of blocks, each of which intersects each of two given non-intersecting blocks, as well as algorithms for constructing block designs in general. The algorithms are given in two notations - algebraic and numeric, i.e. with representation of inputs and outputs by identifiers of elements or blocks or by numbers of these identifiers at a certain numbering by initial non-negative integers. For this purpose, the corresponding numbering algorithms and numbering inversion algorithms are used. #COMESYSO1120