Super-simple (v, 4, 2) directed designs and a lower bound for the minimum size of their defining set

TL;DR

This paper proves the existence of super-simple (v, 4, 2) directed designs for all v mod 3 and establishes a lower bound on the size of their defining sets, contributing to combinatorial design theory.

Contribution

It demonstrates the existence of super-simple (v, 4, 2) directed designs for all relevant v and provides a lower bound for the size of their defining sets, advancing design theory.

Findings

Existence of super-simple (v, 4, 2) directed designs for all v mod 3.

Each such design has a defining set with at least half of the blocks.

Provides a lower bound for the size of defining sets in these designs.

Abstract

In this paper, we show that for all v\pmod 1 (mod 3), there exists a super- simple (v, 4, 2) directed design. Also, we show that for these parameters there exists a super-simple (v, 4, 2) directed design whose each defining set has at least a half of the blocks.