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<?xml version="1.0"?>
<list_of_designs
design_type="block_design"
dtrs_protocol="2.0"
no_designs="1"
pairwise_nonisomorphic="true"
xmlns="http://designtheory.org/xml-namespace">
<info>
<software>
[ DESIGN-1.1, GRAPE-4.2, GAPDoc-0.9999, GAP-4.4.3 ]
</software>
<software>
[ bdstat-0.8/280, numarray-1.1.1, pydesign-0.5/274, python-2.4.0.final.0 ]
</software>
<software>
[ bdtool-0.2/279, pydesign-0.5/274, python-2.4.0.final.0 ]
</software>
</info>
<designs>
<block_design
b="2"
id="v2-b2-k2-0"
v="2">
<blocks ordered="true">
<block>
<z>0</z>
<z>1</z>
</block>
<block>
<z>0</z>
<z>1</z>
</block>
</blocks>
<indicators>
<repeated_blocks flag="true"/>
<resolvable flag="true"/>
<affine_resolvable
flag="true"
mu="2"/>
<equireplicate
flag="true"
r="2"/>
<constant_blocksize
flag="true"
k="2"/>
<t_design
flag="true"
maximum_t="2"/>
<connected
flag="true"
no_components="1"/>
<pairwise_balanced
flag="true"
lambda="2"/>
<variance_balanced flag="true"/>
<efficiency_balanced flag="true"/>
<cyclic flag="true"/>
<one_rotational flag="true"/>
</indicators>
<combinatorial_properties>
<point_concurrences>
<function_on_ksubsets_of_indices
domain_base="points"
k="1"
n="2"
ordered="true"
title="replication_numbers">
<map>
<preimage>
<entire_domain/>
</preimage>
<image>
<z>2</z>
</image>
</map>
</function_on_ksubsets_of_indices>
<function_on_ksubsets_of_indices
domain_base="points"
k="2"
n="2"
ordered="true"
title="pairwise_point_concurrences">
<map>
<preimage>
<entire_domain/>
</preimage>
<image>
<z>2</z>
</image>
</map>
</function_on_ksubsets_of_indices>
</point_concurrences>
<block_concurrences>
<function_on_ksubsets_of_indices
domain_base="blocks"
k="1"
n="2"
ordered="unknown"
title="block_sizes">
<map>
<preimage_cardinality>
<z>2</z>
</preimage_cardinality>
<image>
<z>2</z>
</image>
</map>
</function_on_ksubsets_of_indices>
<function_on_ksubsets_of_indices
domain_base="blocks"
k="2"
n="2"
ordered="unknown"
title="pairwise_block_intersection_sizes">
<map>
<preimage_cardinality>
<z>1</z>
</preimage_cardinality>
<image>
<z>2</z>
</image>
</map>
</function_on_ksubsets_of_indices>
</block_concurrences>
<t_design_properties>
<parameters
b="2"
k="2"
lambda="2"
r="2"
t="2"
v="2"/>
<square flag="true"/>
<projective_plane flag="false"/>
<affine_plane flag="false"/>
<steiner_system flag="false"/>
<steiner_triple_system flag="false"/>
</t_design_properties>
<alpha_resolvable>
<index_flag
flag="true"
index="2"/>
</alpha_resolvable>
<t_wise_balanced>
<index_flag
flag="true"
index="1"/>
<index_flag
flag="true"
index="2"/>
</t_wise_balanced>
</combinatorial_properties>
<automorphism_group>
<permutation_group
degree="2"
domain="points"
order="2">
<generators>
<permutation>
<z>1</z>
<z>0</z>
</permutation>
</generators>
<permutation_group_properties>
<primitive flag="true"/>
<generously_transitive flag="true"/>
<multiplicity_free flag="true"/>
<stratifiable flag="true"/>
<no_orbits value="1"/>
<degree_transitivity value="2"/>
<rank value="2"/>
<cycle_type_representatives>
<cycle_type_representative>
<permutation>
<z>1</z>
<z>0</z>
</permutation>
<cycle_type ordered="true">
<z>2</z>
</cycle_type>
<no_having_cycle_type>
<z>1</z>
</no_having_cycle_type>
</cycle_type_representative>
<cycle_type_representative>
<permutation>
<z>0</z>
<z>1</z>
</permutation>
<cycle_type ordered="true">
<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="not_applicable"/>
<no_block_orbits value="not_applicable"/>
<degree_block_transitivity value="not_applicable"/>
</automorphism_group_properties>
</automorphism_group>
<resolutions
all_classes_represented="true"
pairwise_nonisomorphic="true">
<resolution>
<function_on_indices
domain="blocks"
n="2"
ordered="true"
title="resolution">
<map>
<preimage>
<z>0</z>
</preimage>
<image>
<z>0</z>
</image>
</map>
<map>
<preimage>
<z>0</z>
</preimage>
<image>
<z>1</z>
</image>
</map>
</function_on_indices>
<automorphism_group>
<permutation_group
degree="2"
domain="points"
order="2">
<generators>
<permutation>
<z>1</z>
<z>0</z>
</permutation>
</generators>
</permutation_group>
</automorphism_group>
</resolution>
</resolutions>
<statistical_properties precision="9">
<canonical_variances
no_distinct="1"
ordered="true">
<value multiplicity="1">
<d>0.5</d>
</value>
</canonical_variances>
<pairwise_variances>
<function_on_ksubsets_of_indices
domain_base="points"
k="2"
n="2"
ordered="true">
<map>
<preimage>
<entire_domain/>
</preimage>
<image>
<d>1.0</d>
</image>
</map>
</function_on_ksubsets_of_indices>
</pairwise_variances>
<optimality_criteria>
<phi_0>
<value>
<d>-0.693147181</d>
</value>
<absolute_efficiency>
<z>1</z>
</absolute_efficiency>
<calculated_efficiency>
<z>1</z>
</calculated_efficiency>
</phi_0>
<phi_1>
<value>
<d>0.5</d>
</value>
<absolute_efficiency>
<z>1</z>
</absolute_efficiency>
<calculated_efficiency>
<z>1</z>
</calculated_efficiency>
</phi_1>
<phi_2>
<value>
<d>0.25</d>
</value>
<absolute_efficiency>
<z>1</z>
</absolute_efficiency>
<calculated_efficiency>
<z>1</z>
</calculated_efficiency>
</phi_2>
<maximum_pairwise_variances>
<value>
<d>1.0</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>0.5</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>4.0</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="1">
<d>1.0</d>
</value>
</canonical_efficiency_factors>
<functions_of_efficiency_factors>
<harmonic_mean alias="A">
<value>
<d>1.0</d>
</value>
</harmonic_mean>
<geometric_mean alias="D">
<value>
<d>1.0</d>
</value>
</geometric_mean>
<minimum alias="E">
<value>
<d>1.0</d>
</value>
</minimum>
</functions_of_efficiency_factors>
</statistical_properties>
</block_design>
</designs>
</list_of_designs>
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