Methods used in current tables
| Dynamic programming construction | 3130
|
| Simple construction | 1410
|
unknown | 1067
| | Private tools | 925
|
| Multiple | 736
|
| Lex covering | 258
|
| Simulated annealing | 237
|
| Constructed | 232
|
| Dynamic programming covering | 140
|
| Simple construction: combined | 117
|
| Simple construction: multiple | 70
|
| Simple construction: induced | 67
|
| Lexicographic greedy covering | 58
|
| Dynamic construction | 55
|
| Wheel generator | 51
|
| Cyclic covering | 35
|
| Elaborated | 33
|
| Simple construction: deleted element | 31
|
| Tabu search | 29
|
| Private tool | 27
|
| Random greedy covering | 23
|
| Cyclic covering found by search program | 20
|
| Simple construction: added element to c(v-1,k-1,t) covering | 18
|
| Steiner quadruple system | 16
|
| Sidorenko construction | 15
|
| Simple optimization | 12
|
| Dynamic programming | 12
|
| Constructed using simulated annealing | 11
|
| Design is based on c (v - 1, k, t) = b - v | 10
|
| Cyclic construction | 10
|
| Simulated annealing covering | 9
|
| Sidorenko method | 9
|
| See paper by jrj abel et al. in discrete mathematics 307 (2007) | 9
|
| Cyclic covering found by a search program | 9
|
| Own program & ininuga | 8
|
| Nurmela and ostergard simulated annealing cover | 8
|
| Nurmela-ostergard symmetric covering | 7
|
| Affine geometry covering | 7
|
| Induced | 6
|
| Covering provided by rade belic | 6
|
| Steiner triple system | 5
|
| Simple combine | 5
|
| Extraction/remainder | 5
|
| Colex greedy covering | 5
|
| Simple method construction | 4
|
| Simple construction: added element to c(v,k-1,t) covering | 4
|
| Nurmela-ostergard simulated annealing covering design | 4
|
| Constructed using difference families | 4
|
| Steiner system | 3
|
| Reverse engineering smaller systems | 3
|
| Projective plane | 3
|
| Modified cover32 routine by dietmar pree | 3
|
| Mills, jcta 13 (1972) pp. 55-78. | 3
|
| Mills, ars combinatoria, 8 (1979) pg. 247 | 3
|
| Mills, ars combinatoria, 8 (1979) pg. 231 | 3
|
| Mills, ars combinatoria 8 (1979) pp. 199-315 | 3
|
| Found by a hill-climbing program | 3
|
| Cyclic symmetry | 3
|
| Cyclic steiner system | 3
|
| Covering provided by alex sidorenko (personal communication) | 3
|
| Covering found by a hill-climbing program | 3
|
| Constructed using dynamic programming | 3
|
| Steiner system (derived) | 2
|
| Several methods (including sa) | 2
|
| Nurmela-ostergard simulated annealing covering | 2
|
| Jcd 1998, pp. 21-41 | 2
|
| Hill-climb on cyclic orbits | 2
|
| Hill-climb on affine orbits | 2
|
| From 81,25,5 | 2
|
| Covering provided by john cock (personal communication) | 2
|
| Covering provided by dietmar pree | 2
|
| Covering pairs by quads: mills, jcta 15:138-166, 1973. | 2
|
| Constructed using difference sets | 2
|
| Constructed by simulated annealing | 2
|
| Communicated by d. todorov, using pg(2,4) | 2
|
| Communicated by d. todorov, using pg(2,3) | 2
|
| Affine plane | 2
|
| Using td(6,16) and 6*modified c(18,6,2,2) | 1
|
| Using td(6,15) and 6*modified c(18,6,2,2) | 1
|
| Using resolvable c(72,4,2), see lamken, mullen and rees (jcd, 1997-1) | 1
|
| Using resolvable c(68,4,2), see lamken, mullen and rees (jcd, 1997-1) | 1
|
| Using rc(63,3,2) | 1
|
| Using rc(60,3,2) by lamken and mills (1993) | 1
|
| Using rc(54,3,2) | 1
|
| Using rc(45,3,2) | 1
|
| Using rc(42,3,2) | 1
|
| Using ininuga, by uros boltin | 1
|
| Using dietmar pree version | 1
|
| Using a (v,4,22*)-pbd and c(22,4,2) | 1
|
| Unusual methods | 1
|
| Tripling a resolvable c(25,5,2) | 1
|
| Td(7,13) and 7 * modified c(15,7,2) | 1
|
| Td(4,24) + 4*c(27,4,2) | 1
|
| Td(4,24) + 4 * c(26,4,2) | 1
|
| Td(4,23) + 4 * c(25,4,2) | 1
|
| Td(4,19) & 4 * c(21,4,2) | 1
|
| Td(4,18) + 4 * c(21,4,2) | 1
|
| Td(4,15) and 4 * modified c(18,4,2) | 1
|
| Td(4,12) & 4 * c(15,4,2) | 1
|
| Superfluous-element hill climb on a random greedy covering | 1
|
| Superfluous-element hill climb on a covering | 1
|
| Steiner system, taken | 1
|
| Simualted annealing | 1
|
| Simple construction: | 1
|
| Several methods (including simulated annealing) | 1
|
| See paper in journal | 1
|
| See designs, codes and cryptography 17 (1999), 181-186 | 1
|
| Reverse engineering | 1
|
| Produced with covermaster (by john rawson), wheelgenerator (by anastasios tampakis) and private tools. | 1
|
| Privat tools | 1
|
| Normal methods | 1
|
| Mills, ars combinatoria, 8 (1979) pg. 270 | 1
|
| Mills, ars combinatoria, 8 (1979) pg. 254 | 1
|
| Mill, jcta 15 (1973) 138-166 | 1
|
| Ininuga (by uros boltin) | 1
|
| From td(9,9) and 9*c(14,9,2,2,3) with 5 holes | 1
|
| From td(7,12) and 7*c(15,7,2,2,6) with 3 holes | 1
|
| From td(7,12) and 7*c(13,7,2,2,5) with 2 holes | 1
|
| From td(6,13) and 6*c(16,6,2,2,10) | 1
|
| From 77,25,5 | 1
|
| From 76,25,5 | 1
|
| From 73,25,5 | 1
|
| From 69,15,3 | 1
|
| From 57,8,2 | 1
|
| From 24,18,8 | 1
|
| From 1-flat on 42 numbers | 1
|
| Ex 8 | 1
|
| Ex 15 | 1
|
| Ex 13 | 1
|
| Doubling resolvable c(25,5,2) | 1
|
| Doubling c(42,4,3) | 1
|
| Doubling c(36,4,3) | 1
|
| Doubling c(30,4,3) | 1
|
| Doubling c(18,4,3) | 1
|
| Cyclic symmetrical | 1
|
| Cyclic covering on z5*z7 | 1
|
| Cyclic covering on z3*z17 with one point at infinity | 1
|
| Cyclic | 1
|
| Covering provided by konstantin katskov, found by exhaustive search | 1
|
| Covering produced by floyd l. oats, using a ranking and reduction process | 1
|
| Covering pairs by quints, mullin, jcmcc 2:133-146, 1987 | 1
|
| Covering pairs by quints, mills & mullin, jcta 49:308-322, 1988 | 1
|
| Covering found by rade belic | 1
|
| Covering found by john rawson | 1
|
| Covering | 1
|
| Construction combined | 1
|
| Communicated by d. todorov | 1
|
| Combinado | 1
|
| Block-array construction (gordon, patashnik, petro and taylor) | 1
|
| Block covering | 1
|