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Extra resources for Designs 2002: Further Computational and Constructive Design Theory

Sample text

1. 5. 2 There exists a CODLS(v, 3) for all 11 :::; v :::; 49 and v odd and v = 61, except possibly v = 11. 3. 5. 3. 8. 6. The disjoint subsets come from the groups and a block of size 7. 6. The disjoint subsets consist of the groups, if n is even. If n is odd, the disjoint subsets come from the groups and a block of size five, where we take the first four groups minus the intersection points with the five block, the intersection points of the first four groups with the five block, and the unique group of size three.

A group divisible design (GDD) GD[K, 1, M; v] is a triple (X, 9, 13) where 1 X is a v-set (of points), 2 9 is a collection of nonempty subsets of X (called groups) with cardinality in M and which partition X, 3 13 is a collection of subsets of X (called blocks) with cardinality at least two in K, 4 no block intersects any group in more than one point, 5 each pair set {x, y} of points not contained in a group is contained in exactly one block. The group-type (or type) of the GDD (X, 9, 13) is the multiset of sizes IGI of the G E 9 and we usually use the "exponential" notation for its description: group-type 1i 2j 3k ...

6. The disjoint subsets come from the groups and a block of size 7. 6. The disjoint subsets consist of the groups, if n is even. If n is odd, the disjoint subsets come from the groups and a block of size five, where we take the first four groups minus the intersection points with the five block, the intersection points of the first four groups with the five block, and the unique group of size three. For the case v = 33, we start with an RGD[5, 1,7; 35] and delete a block to obtain a GD[{4,5},1,6;30] with a parallel class of blocks of size five.

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