A Simple Example

We start with a simple example. It is a list of designs, in our external representation, containing a single design, known as the Fano plane.

<list_of_designs design_type="block_design" dtrs_protocol="1.1" no_designs="1"
 pairwise_nonisomorphic="true" xmlns="http://designtheory.org/xml-namespace">
    <block_design b="7" id="t2-v7-k3-L1-1" v="7">
        <blocks ordered="true">
            <block><z>0</z><z>1</z><z>2</z></block>
            <block><z>0</z><z>3</z><z>4</z></block>
            <block><z>0</z><z>5</z><z>6</z></block>
            <block><z>1</z><z>3</z><z>5</z></block>
            <block><z>1</z><z>4</z><z>6</z></block>
            <block><z>2</z><z>3</z><z>6</z></block>
            <block><z>2</z><z>4</z><z>5</z></block>
        </blocks>
    </block_design>
</list_of_designs>

The design is described in XML. Later in this document we discuss why we have chosen XML for the specification of block designs. For now, if you stare at the code, you will see that, at the first level of indentation, between the opening and closing tags block_design, we have indeed specified the design: it has $v = 7$ points, $b = 7$ blocks, and the seven blocks are listed (the first one is $[0,1,2]$, and there are tags to identify each of 0,1,2 as an integer). There is also a identification string for the design.

In XML, there are two ways of providing information, which we refer to as ``attributes'' and ``elements''. An ``attribute'', such as v, b or id, occurs within a tag, whereas an ``element'', such as blocks occurs within the scope of the tag. An XML document has the structure of a tree; the elements are the nodes of the tree, and the attributes are associated with nodes. We will use the general term ``properties'' in something like its mathematical sense, describing both attributes and elements.

This document contains our specification of an ``external representation'' of block designs, together with an explanation of the terms used, and some justification for doing it in the way we have chosen.