2-(31,6,1) : Nests for 2 smallest defining sets added. 2-(31,15,7): Minimal = smallest for PG42. 4-(11,5,1) : Nests for 42 smallest defining sets added. Added copyrights.
4-(11,5,1) : Now have nests for 119 smallest defining sets and all length
6 minimal defining sets are listed.
4-(11,5,1) : Now have nests for all 216 smallest defining sets.
2-(31,6,1) : Now know there are 6 smallest defining sets of length 11
and 61 other minimal defining sets of length 12. The nests
for the 6 smallest defining sets and 1 of the other minimal
defining sets have been determined. Defining sets are now
all ordered.
2-(31,15,7): The nest for one smallest QuadRes defining set and a list of
248 smallest defining sets (of length 9) of an estimated
120 000, and one other minimal defining set added.
2-(31,6,1) : Nests for all 67 known minimal defining sets now included.
2-(15,3,1) : Examples of nondefining sets S for which Aut S <= Aut D added.
2-(31,6,1) : The list of 67 known minimal defining sets is now known to be
a complete list.
2-(25,5,1) : Nests for 27 (of an estimated 4000) smallest defining sets
added.
2-(9,3,1) : i-sets of disjoint designs added.
2-(9,3,1) : i-sets of disjoint designs refined: better navigation,
automorphism groups and orbit-lengths added.
*-(*,*,*) : `#CommonBlocks' now reads `#BlocksCommonToAllCompletions'.
2-(15,7,3): D1 : 1st defining set: Aut S is nonabelian (of order 21).
D4 : 1st, 4th, 6th defining sets : Aut S = Z_2 x Z_2.
5th defining set: Aut S is dihedral.
7th defining set: Aut S = S_3 x S_3.
D5 : 1st defining set: Aut S = S_3 wr Z_2 = (S_3 x S_3).2.
2nd defining set: Aut S = S_5.
2-(13,4,1): D1 : 1st defining set: Aut S = S_4.
2-(16,4,1): D1 : 1st defining set: Aut S is dihedral.
2nd defining set: Aut S = S_3.
4th defining set: Aut S = Z_2 x Z_2.
11th defining set: Aut S = Z_4.
12th defining set: Aut S = S_3.
2-(10,4,4) : The nest of one defining set of length 17 added.
2-(10,4,4) : The nest of one smallest defining set (of length 16) added.
2-(9,3,1) : Maximality of each i-set determined.
2-(6,3,4) : Minimal defining sets only, added.
2-(7,3,3) : Minimal defining sets only, added.
2-(7,3,2) : Minimal defining sets only, added.
2-(7,3,2) : Minimal defining sets (only), of the non-simple designs
D2, D3 and D4, added. Automorphism groups of each defining
set of all four designs, added.
2-(6,3,4) : Previous D1 on point-set {1 .. 6} renamed D1'. D1 redone
on the point-set {0 .. 5} with block labelling matching
that of the 2-(6,3,2) design D1. The non-simple designs
D2, D3 and D4, (also on {0 .. 5}, added. Minimal defining
sets and automorphism groups of each defining set (only)
of D1 to D4, are included.
2-(7,3,3) : The one simple and 9 other non-simple designs complete
with automorphism groups for each defining set, added.
2-(7,3,2) : All four designs redone, so that each is now of form
F U F^g for some permutation g. In essence this means
D1, D3 and D4 have changed. Due to an error in the
calculation of the automorphism group for D4 the number
of defining sets has apparently grown from 5 to 8
i.e. the blocks automorphism group was calculated to be
larger than it should have been and some defining sets
were missed.
2-(7,3,2) : Some check statistics added ... however, since orbits
of non-defining sets need not be subsets of our check-
list the totals are somewhat meaningless.
2-(7,3,2) : All redone with meaningful check statistics added.
2-(7,3,3) : D2 and D3 redone with check statistics included.
2-(6,3,4) : All redone with meaningful check statistics added.
D1' has been deleted. The previous versions had many errors.
2-(7,3,3) : D4, D5, D6 and D7 redone with check statistics included.
D8, D9 and D10 redone but no check statistics available, yet.
2-(7,3,3) : D10 check statistics added.
2-(7,3,3) : D9 check statistics added.
2-(7,3,3) : D8 check statistics added.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
reducible designs added.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
irreducible designs: K4, K5, K8, K9, K12, K13, K16, K21,
K25, K27, K32, K33, K35, K36 added.
K1 and K2 have been redone to included check statistics.
2-(9,3,2) : K1 redone yet again: now has check statistics for all
minimal defining sets (and the formatting and ordering
is sensible).
Check statistics have been added for designs K3, K6, K7,
K14, K15, K23 and K29 (now the reducible designs other than
K1 have the fullest possible information for *smallest*,
but not minimal defining sets).
Smallest defining sets and their automorphism groups of
irreducible designs: K11, K20 added.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
irreducible designs: K10, K17, K18, K24 added.
K2 now has all minimal defining sets along with check
statistics.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
irreducible designs: K19, K28 added.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
irreducible designs: K22, K26, K31, K34 added.
2-(9,3,2) : Smallest defining sets and their automorphism groups of
irreducible design: K30 added.
2-(9,3,2) : K3 now has all minimal defining sets along with check
statistics.
2-(9,3,2) : K14 now has all minimal defining sets along with check
statistics.
2-(11,5,2) : Removed question. (There is a unique design for these
parameters.)
Added Table of Contents.
Added links to `Outline of nests programs'.
2-(6,3,2) : Sorted N''.
2-(6,3,4) : Added nests.
2-(7,3,1) : Sorted N''.
2-(7,3,2) : Added nests.
2-(8,4,3) : Sorted N''.
2-(9,3,1) : Sorted N''.
2-(10,4,2) : Sorted N''.
2-(10,4,4) : Amended and sorted N''.
2-(11,5,2) : Sorted N''.
2-(13,3,1) : Sorted N''.
2-(13,4,1) : Sorted N''.
2-(15,7,3) : Sorted N''.
2-(16,4,1) : Sorted N''.
2-(16,6,2) : Sorted N''.
2-(21,5,1) : Sorted N''.
3-(8,4,1) : Sorted N''.
2-(7,3,3) : Added nests for designs D1, ..., D8, and for most of the
minimal defining sets of D9.
2-(31,15,7) : Added N'' to PG42 design.
2-(7,3,3) : Added nests for design D10.
2-(15,3,1) : Sorted N''. Added Colin Ramsay -> Tony Ramsay point set
map.
4-(11,5,1) : Sorted N''.
2-(15,3,1) : Added (and later same day corrected - each block needed
to be sorted) nests for design P3 which is isomorphic to
W1. The labelling (chosen by Moran et al) was convenient
for finding minimal defining sets ... all are given,
whereas only 1 is given for W1.
2-(19,9,4) : Nests for complete list of minimal defining sets added.
2-(23,11,5) : Nests for 14 smallest defining sets and the complete
list of 396 smallest defining sets, and probably all
other minimal defining sets (221 9-sets) added.
2-(23,11,5) : Nests for 31 more smallest defining sets added.
2-(23,11,5) : Nests for 46 more smallest defining sets added.
2-(23,11,5) : Now have nests for 321 smallest defining sets.
2-(23,11,5) : Now have nests for all minimal defining sets.
Last update: 30 May, 2002
Greg Gamble