Ordering the blocks of a design, the point sum of an element is the sum of the indices of blocks containing that element. Block labelling for popularity asks for the point sums to be as equal as possible. For Steiner systems of order v strength t in general, the average point sum is O(v(2t-1)); under various restrictions on block partitions of the Steiner system, the difference between the largest and smallest point sums is shown to be O(v((t+1)/2) log v).
Many distributed ledger technologies (DLT) offer smart contract platforms, that are already used in various industries such as healthcare, transportation, government, banking, and insurance. Software Lifecycle Management (SLM) is another area where DLT and smart contract platforms could play an important role in the future. SLM processes are covering the initial setup, technical and business configuration and ongoing maintenance of software systems that often consist of many cloud services, on-premise servers, and/or edge devices, spread on many geographical locations. In SLM there are many participants that should communicate each other to achieve common goal, for example the software provisioning. In case something wrong happens in their communication, it is very hard to prove what is the reason and which party failed to deliver, since the environment is complex and the protocols of responsibilities are not bound to the software dependencies. The purpose of this paper is to demonstrate how DLT-based smart contract platforms supports SLM processes for complex business systems where various participants are involved.
In this paper we consider the problem of class with parameters (q(3) 2q(2)+ q + 2, q(2)+ 2q + 2) in PG(3, q). Such arcs correspond to Griesmer [q(3) + 2q(2) + q + 2, 4, q(3) + q(2) - q](q)- codes. They are trivially obtained as the sum of a maximal cap in PG(3, q) and the whole geometry. We prove that for q = 5, 7 this is the only possible construction. This was known to be the case also for q = 4. For q = 3, there exists one further example. The characterization uses a divisibility result for plane blocking sets with parameters (q(2), q - 1) which is of independent interest.
The boom of public blockchains and smart contract platforms opened new approaches to solve existing issues. These new approaches addressed successfully some weaknesses of previous processes and created some new classes of problems that need solutions. In this paper we explore distributed system based on smart contract platform with a low-entry barrier designed for direct incentivization of results of scientific research. The proposed system relies on transparent interactions between organizations and individual scientist defining hard computational problems with others that are willing to invest time and efforts searching for computational solutions.
In this paper we present new upper bounds on the size of an arc in the projective Hjelslev planes PHG(2, R), where R is a chain ring of mutilicity index 2.
