Simple Kirkman Packing Designs \(SKPD({3, 4}, v)\) with Index Two

Abstract

A simple Kirkman packing design \(SKPD(\{w, w+1\}, v)\) with index \(\lambda\) is a resolvable packing with distinct blocks and maximum possible number of parallel classes, each containing \(u =v-w \lfloor \frac{v}{w} \rfloor\) blocks of size \(w+1\) and \(\frac{v-u(w+1)}{w}\) blocks of size \(w\), such that each pair of distinct elements occurs in at most \(\lambda\) blocks. In this paper, we solve the spectrum of simple Kirkman packing designs \(SKPD(\{3, 4\}, v)\) with index \(2\) completely.