This site is to host a searchable database of combinatorial and statistical designs. The DesignDB project is an offshoot of the research started at DesignTheory.org. While the original site contains mainly static and textual content, our focus is on providing dynamic content and direct application services. The database is under intensive development although it is not ready for public use yet.
There is, however, a limited experimental prototype running which contains only t-designs at the moment.DesignDB uses JSON for the external representation of designs, that is when designs are written or read in/from files or exchanged between applications. This format is based on the original ext-rep specification created in an earlier phase at DesignTheory.org. In particular, the new format provides exactly the same mathematical content but uses JSON instead of XML. The new specification will be published soon.
Here is an example showing the only resolvable 2-(8,4,3) design.
{
"block_design" : {
"id" : "t2-v8-b14-r7-k4-L3-3",
"v" : 8,
"b" : 14,
"blocks" : [
[0, 1, 2, 3], [0, 1, 4, 5], [0, 1, 6, 7], [0, 2, 4, 6], [0, 2, 5, 7],
[0, 3, 4, 7], [0, 3, 5, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 3, 4, 6],
[1, 3, 5, 7], [2, 3, 4, 5], [2, 3, 6, 7], [4, 5, 6, 7]
],
"indicators" : {
"repeated_blocks" : false,
"resolvable" : true,
"affine_resolvable" : {
"mu" : 2
},
"equireplicate" : {
"r" : 7
},
"constant_blocksize" : {
"k" : 4
},
"t_design" : {
"maximum_t" : 3
},
"connected" : {
"no_components" : 1
},
"pairwise_balanced" : {
"lambda" : 3
},
"variance_balanced" : true,
"efficiency_balanced" : true,
"cyclic" : false,
"one_rotational" : true
},
"combinatorial_properties" : {
"point_concurrences" : [
{
"domain_base" : "points",
"n" : 8,
"k" : 1,
"ordered" : true,
"title" : "replication_numbers",
"maps" : [
{
"preimage" : ["entire_domain"],
"image" : 7
}
]
},
{
"domain_base" : "points",
"n" : 8,
"k" : 2,
"ordered" : true,
"title" : "pairwise_point_concurrences",
"maps" : [
{
"preimage" : ["entire_domain"],
"image" : 3
}
]
},
{
"domain_base" : "points",
"n" : 8,
"k" : 3,
"ordered" : true,
"maps" : [
{
"preimage" : ["entire_domain"],
"image" : 1
}
]
}
],
"block_concurrences" : [
{
"domain_base" : "blocks",
"n" : 14,
"k" : 1,
"ordered" : "unknown",
"title" : "block_sizes",
"maps" : [
{
"preimage_cardinality" : 14,
"image" : 4
}
]
},
{
"domain_base" : "blocks",
"n" : 14,
"k" : 2,
"ordered" : "unknown",
"title" : "pairwise_block_intersection_sizes",
"maps" : [
{
"preimage_cardinality" : 84,
"image" : 2
},
{
"preimage_cardinality" : 7,
"image" : 0
}
]
}
],
"t_design_properties" : {
"parameters" : {
"t" : 2,
"v" : 8,
"b" : 14,
"r" : 7,
"k" : 4,
"lambda" : 3
},
"square" : false,
"projective_plane" : false,
"affine_plane" : false,
"steiner_system" : {
"t" : 3
},
"steiner_triple_system" : false
},
"alpha_resolvable" : [
{
"index" : 7,
"flag" : true
}
],
"t_wise_balanced" : [
{
"index" : 1,
"flag" : true
},
{
"index" : 2,
"flag" : true
},
{
"index" : 3,
"flag" : true
}
]
},
"automorphism_group" : {
"permutation_group" : {
"degree" : 8,
"order" : 1344,
"domain" : "points",
"generators" : [
[2, 3, 0, 1, 6, 7, 4, 5], [1, 0, 2, 3, 4, 5, 7, 6],
[0, 1, 3, 2, 5, 4, 6, 7], [1, 0, 3, 2, 4, 5, 6, 7],
[0, 1, 3, 2, 7, 6, 4, 5], [0, 2, 3, 1, 6, 4, 5, 7],
[0, 1, 5, 4, 3, 2, 6, 7]
],
"permutation_group_properties" : {
"primitive" : true,
"generously_transitive" : true,
"multiplicity_free" : true,
"stratifiable" : true,
"no_orbits" : 1,
"degree_transitivity" : 3,
"rank" : 2,
"cycle_type_representatives" : [
{
"permutation" : [0, 2, 4, 6, 3, 1, 7, 5],
"cycle_type" : [1, 7],
"no_having_cycle_type" : 384
},
{
"permutation" : [3, 2, 7, 6, 5, 4, 1, 0],
"cycle_type" : [2, 6],
"no_having_cycle_type" : 224
},
{
"permutation" : [4, 5, 6, 7, 1, 0, 3, 2],
"cycle_type" : [4, 4],
"no_having_cycle_type" : 252
},
{
"permutation" : [0, 1, 3, 2, 6, 7, 5, 4],
"cycle_type" : [1, 1, 2, 4],
"no_having_cycle_type" : 168
},
{
"permutation" : [0, 1, 4, 5, 6, 7, 2, 3],
"cycle_type" : [1, 1, 3, 3],
"no_having_cycle_type" : 224
},
{
"permutation" : [2, 3, 0, 1, 6, 7, 4, 5],
"cycle_type" : [2, 2, 2, 2],
"no_having_cycle_type" : 49
},
{
"permutation" : [0, 1, 2, 3, 5, 4, 7, 6],
"cycle_type" : [1, 1, 1, 1, 2, 2],
"no_having_cycle_type" : 42
},
{
"permutation" : [0, 1, 2, 3, 4, 5, 6, 7],
"cycle_type" : [1, 1, 1, 1, 1, 1, 1, 1],
"no_having_cycle_type" : 1
}
]
}
},
"automorphism_group_properties" : {
"block_primitive" : false,
"no_block_orbits" : 1,
"degree_block_transitivity" : 1
}
},
"resolutions" : {
"pairwise_nonisomorphic" : true,
"all_classes_represented" : true,
"value" : [
{
"function_on_indices" : {
"n" : 14,
"ordered" : true,
"title" : "resolution",
"maps" : [
{
"preimage" : [0, 13],
"image" : 0
},
{
"preimage" : [1, 12],
"image" : 1
},
{
"preimage" : [2, 11],
"image" : 2
},
{
"preimage" : [3, 10],
"image" : 3
},
{
"preimage" : [4, 9],
"image" : 4
},
{
"preimage" : [5, 8],
"image" : 5
},
{
"preimage" : [6, 7],
"image" : 6
}
]
},
"automorphism_group" : {
"permutation_group" : {
"degree" : 8,
"order" : 1344,
"domain" : "points",
"generators" : [
[1, 0, 3, 2, 5, 4, 7, 6], [2, 3, 0, 1, 6, 7, 4, 5],
[5, 4, 7, 6, 1, 0, 3, 2], [1, 0, 2, 3, 4, 5, 7, 6],
[1, 0, 2, 3, 4, 5, 7, 6], [1, 0, 3, 2, 4, 5, 6, 7],
[1, 0, 2, 3, 6, 7, 5, 4], [3, 1, 0, 2, 5, 7, 6, 4],
[0, 1, 5, 4, 3, 2, 6, 7]
]
}
}
}
]
}
}
}
All the designs available at DesignTheory.org have been converted into the new format. For reference purposes, we provide this collection of designs as compressed files until our DesignDB goes online.
Contact: info at designdb dot org