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An example

Here in its entirety is the example which we have seen in parts throughout this document.

<?xml version="1.0"?>
<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>
        <indicators>
            <repeated_blocks flag="false">
            </repeated_blocks>
            <resolvable flag="false">
            </resolvable>
            <affine_resolvable flag="false">
            </affine_resolvable>
            <equireplicate flag="true" r="3">
            </equireplicate>
            <constant_blocksize flag="true" k="3">
            </constant_blocksize>
            <t_design flag="true" maximum_t="2">
            </t_design>
            <connected flag="true" no_components="1">
            </connected>
            <pairwise_balanced flag="true" lambda="1">
            </pairwise_balanced>
            <variance_balanced flag="true">
            </variance_balanced>
            <efficiency_balanced flag="true">
            </efficiency_balanced>
            <cyclic flag="true">
            </cyclic>
            <one_rotational flag="false">
            </one_rotational>
        </indicators>
        <combinatorial_properties>
            <point_concurrences>
                <function_on_ksubsets_of_indices domain_base="points" k="1"
                 n="7" ordered="true" title="replication_numbers">
                    <map>
                        <preimage>
                            <entire_domain>
                            </entire_domain>
                        </preimage>
                        <image><z>3</z></image>
                    </map>
                </function_on_ksubsets_of_indices>
                <function_on_ksubsets_of_indices domain_base="points" k="2"
                 n="7" ordered="true" title="pairwise_point_concurrences">
                    <map>
                        <preimage>
                            <entire_domain>
                            </entire_domain>
                        </preimage>
                        <image><z>1</z></image>
                    </map>
                </function_on_ksubsets_of_indices>
            </point_concurrences>
            <block_concurrences>
                <function_on_ksubsets_of_indices domain_base="blocks" k="1"
                 n="7" ordered="unknown" title="block_sizes">
                    <map>
                        <preimage_cardinality><z>7</z></preimage_cardinality>
                        <image><z>3</z></image>
                    </map>
                </function_on_ksubsets_of_indices>
                <function_on_ksubsets_of_indices domain_base="blocks" k="2"
                 n="7" ordered="unknown"
                 title="pairwise_block_intersection_sizes">
                    <map>
                        <preimage_cardinality><z>21</z></preimage_cardinality>
                        <image><z>1</z></image>
                    </map>
                </function_on_ksubsets_of_indices>
            </block_concurrences>
            <t_design_properties>
                <parameters b="7" k="3" lambda="1" r="3" t="2" v="7">
                </parameters>
                <square flag="true">
                </square>
                <projective_plane flag="true">
                </projective_plane>
                <affine_plane flag="false">
                </affine_plane>
                <steiner_system flag="true" t="2">
                </steiner_system>
                <steiner_triple_system flag="true">
                </steiner_triple_system>
            </t_design_properties>
            <alpha_resolvable>
                <index_flag flag="true" index="3">
                </index_flag>
            </alpha_resolvable>
            <t_wise_balanced>
                <index_flag flag="true" index="1">
                </index_flag>
                <index_flag flag="true" index="2">
                </index_flag>
            </t_wise_balanced>
        </combinatorial_properties>
        <automorphism_group>
            <permutation_group degree="7" domain="points" order="168">
                <generators>
                    <permutation>
                        <z>1</z>
                        <z>0</z>
                        <z>2</z>
                        <z>3</z>
                        <z>5</z>
                        <z>4</z>
                        <z>6</z>
                    </permutation>
                    <permutation>
                        <z>0</z>
                        <z>2</z>
                        <z>1</z>
                        <z>3</z>
                        <z>4</z>
                        <z>6</z>
                        <z>5</z>
                    </permutation>
                    <permutation>
                        <z>0</z>
                        <z>3</z>
                        <z>4</z>
                        <z>1</z>
                        <z>2</z>
                        <z>5</z>
                        <z>6</z>
                    </permutation>
                    <permutation>
                        <z>0</z>
                        <z>1</z>
                        <z>2</z>
                        <z>5</z>
                        <z>6</z>
                        <z>3</z>
                        <z>4</z>
                    </permutation>
                    <permutation>
                        <z>0</z>
                        <z>1</z>
                        <z>2</z>
                        <z>4</z>
                        <z>3</z>
                        <z>6</z>
                        <z>5</z>
                    </permutation>
                </generators>
                <permutation_group_properties>
                    <primitive flag="true">
                    </primitive>
                    <generously_transitive flag="true">
                    </generously_transitive>
                    <multiplicity_free flag="true">
                    </multiplicity_free>
                    <stratifiable flag="true">
                    </stratifiable>
                    <no_orbits value="1">
                    </no_orbits>
                    <degree_transitivity value="2">
                    </degree_transitivity>
                    <rank value="2">
                    </rank>
                    <cycle_type_representatives>
                        <cycle_type_representative>
                            <permutation>
                                <z>1</z>
                                <z>3</z>
                                <z>5</z>
                                <z>2</z>
                                <z>0</z>
                                <z>6</z>
                                <z>4</z>
                            </permutation>
                            <cycle_type ordered="true">
                                <z>7</z>
                            </cycle_type>
                            <no_having_cycle_type>
                                <z>48</z>
                            </no_having_cycle_type>
                        </cycle_type_representative>
                        <cycle_type_representative>
                            <permutation>
                                <z>0</z>
                                <z>2</z>
                                <z>1</z>
                                <z>5</z>
                                <z>6</z>
                                <z>4</z>
                                <z>3</z>
                            </permutation>
                            <cycle_type ordered="true">
                                <z>1</z>
                                <z>2</z>
                                <z>4</z>
                            </cycle_type>
                            <no_having_cycle_type>
                                <z>42</z>
                            </no_having_cycle_type>
                        </cycle_type_representative>
                        <cycle_type_representative>
                            <permutation>
                                <z>0</z>
                                <z>3</z>
                                <z>4</z>
                                <z>5</z>
                                <z>6</z>
                                <z>1</z>
                                <z>2</z>
                            </permutation>
                            <cycle_type ordered="true">
                                <z>1</z>
                                <z>3</z>
                                <z>3</z>
                            </cycle_type>
                            <no_having_cycle_type>
                                <z>56</z>
                            </no_having_cycle_type>
                        </cycle_type_representative>
                        <cycle_type_representative>
                            <permutation>
                                <z>0</z>
                                <z>1</z>
                                <z>2</z>
                                <z>4</z>
                                <z>3</z>
                                <z>6</z>
                                <z>5</z>
                            </permutation>
                            <cycle_type ordered="true">
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                                <z>2</z>
                                <z>2</z>
                            </cycle_type>
                            <no_having_cycle_type>
                                <z>21</z>
                            </no_having_cycle_type>
                        </cycle_type_representative>
                        <cycle_type_representative>
                            <permutation>
                                <z>0</z>
                                <z>1</z>
                                <z>2</z>
                                <z>3</z>
                                <z>4</z>
                                <z>5</z>
                                <z>6</z>
                            </permutation>
                            <cycle_type ordered="true">
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                                <z>1</z>
                            </cycle_type>
                            <no_having_cycle_type>
                                <z>1</z>
                            </no_having_cycle_type>
                        </cycle_type_representative>
                    </cycle_type_representatives>
                </permutation_group_properties>
            </permutation_group>
            <automorphism_group_properties>
                <block_primitive flag="true">
                </block_primitive>
                <no_block_orbits value="1">
                </no_block_orbits>
                <degree_block_transitivity value="2">
                </degree_block_transitivity>
            </automorphism_group_properties>
        </automorphism_group>
        <statistical_properties precision="9">
            <canonical_variances no_distinct="1" ordered="true">
                <value multiplicity="6"><d>0.428571429</d></value>
            </canonical_variances>
            <pairwise_variances>
                <function_on_ksubsets_of_indices domain_base="points" k="2"
                 n="7" ordered="true">
                    <map>
                        <preimage>
                            <entire_domain>
                            </entire_domain>
                        </preimage>
                        <image><d>0.857142857</d></image>
                    </map>
                </function_on_ksubsets_of_indices>
            </pairwise_variances>
            <optimality_criteria>
                <phi_0>
                    <value><d>-5.08378716</d></value>
                    <absolute_efficiency><z>1</z></absolute_efficiency>
                    <calculated_efficiency><z>1</z></calculated_efficiency>
                </phi_0>
                <phi_1>
                    <value><d>0.428571429</d></value>
                    <absolute_efficiency><z>1</z></absolute_efficiency>
                    <calculated_efficiency><z>1</z></calculated_efficiency>
                </phi_1>
                <phi_2>
                    <value><d>0.183673469</d></value>
                    <absolute_efficiency><z>1</z></absolute_efficiency>
                    <calculated_efficiency><z>1</z></calculated_efficiency>
                </phi_2>
                <maximum_pairwise_variances>
                    <value><d>0.857142857</d></value>
                    <absolute_efficiency><z>1</z></absolute_efficiency>
                    <calculated_efficiency><z>1</z></calculated_efficiency>
                </maximum_pairwise_variances>
                <E_criteria>
                    <E_value index="1">
                        <value><d>0.428571429</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                    <E_value index="2">
                        <value><d>0.857142857</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                    <E_value index="3">
                        <value><d>1.28571429</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                    <E_value index="4">
                        <value><d>1.71428571</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                    <E_value index="5">
                        <value><d>2.14285714</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                    <E_value index="6">
                        <value><d>2.57142857</d></value>
                        <absolute_efficiency><z>1</z></absolute_efficiency>
                        <calculated_efficiency><z>1</z></calculated_efficiency>
                    </E_value>
                </E_criteria>
            </optimality_criteria>
            <other_ordering_criteria>
                <trace_of_square_of_C>
                    <value><d>32.6666667</d></value>
                    <absolute_comparison><z>1</z></absolute_comparison>
                    <calculated_comparison><z>1</z></calculated_comparison>
                </trace_of_square_of_C>
                <max_min_ratio_canonical_variances>
                    <value><d>1.0</d></value>
                    <absolute_comparison><z>1</z></absolute_comparison>
                    <calculated_comparison><z>1</z></calculated_comparison>
                </max_min_ratio_canonical_variances>
                <max_min_ratio_pairwise_variances>
                    <value><d>1.0</d></value>
                    <absolute_comparison><z>1</z></absolute_comparison>
                    <calculated_comparison><z>1</z></calculated_comparison>
                </max_min_ratio_pairwise_variances>
                <no_distinct_canonical_variances>
                    <value><z>1</z></value>
                    <absolute_comparison><z>1</z></absolute_comparison>
                    <calculated_comparison><z>1</z></calculated_comparison>
                </no_distinct_canonical_variances>
                <no_distinct_pairwise_variances>
                    <value><z>1</z></value>
                    <absolute_comparison><z>1</z></absolute_comparison>
                    <calculated_comparison><z>1</z></calculated_comparison>
                </no_distinct_pairwise_variances>
            </other_ordering_criteria>
            <canonical_efficiency_factors no_distinct="1" ordered="true">
                <value multiplicity="6"><d>0.777777778</d></value>
            </canonical_efficiency_factors>
            <functions_of_efficiency_factors>
                <harmonic_mean alias="A">
                    <value><d>0.777777778</d></value>
                </harmonic_mean>
                <geometric_mean alias="D">
                    <value><d>0.777777778</d></value>
                </geometric_mean>
                <minimum alias="E">
                    <value><d>0.777777778</d></value>
                </minimum>
            </functions_of_efficiency_factors>
        </statistical_properties>
    </block_design>
    <info>
        <creator>
            <software>
                bdstat 0.5/13
            </software>
        </creator>
        <creator>
            <software>
                Design 1.0rev8/51
            </software>
        </creator>
        <reference>
            Any book on combinatorial design theory
        </reference>
        <note>
            Fano plane
        </note>
        <note>
            The unique 2-(7,3,1) up to isomorphism
        </note>
    </info>
</list_of_designs>



Peter Dobcsanyi 2003-12-15