Refined Deterministic Algorithm for Biplane Construction

Abstract

This paper introduces a way of constructing biplanes that uses “filters” in a step prior to an exhaustive computer search, with the objective to make the biplane construction more efficient. The achieved deterministic algorithm classifies biplanes of order 7 and smaller. When performing the search using some additional presumptive conditions, two biplanes of order 9 (k=11) were constructed and a particular inner regularity in the biplane’s structure has been established.