Abstract
The minimum number of blocks having maximum size precisely four that
are required to cover, exactly times, all pairs of elements from a set of
cardinality v is denoted by g(4)
(v) (or g(4)(v) when = 1). All values of
g(4)
(v) are known except for = 1 and v = 17 or 18. It is known that
30 g(4)(17) 31 and 32 g(4)(18) 33. In this paper we show that
g(4)(17) 6= 30 and g(4)(18) 6= 32, thus finalising the determination of g(4)
(v)
for all and v.
1
| Original language | English |
|---|---|
| Pages (from-to) | 303 - 313 |
| Number of pages | 11 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 36 |
| Publication status | Published - 2006 |
| Externally published | Yes |