@article {Mathon:October 2002:0925-1022:119,
	author = "Mathon R.",
	author = "Street A.P.",
	title = "Partitioning Sets of Triples into Small Planes",
	journal = "Designs, Codes and Cryptography",
	volume = "27",
	year = "October 2002",
	abstract = "<P>We study partitions of the set of all {v}\choose{3} triples chosen from a <I>v</I>-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of <I>PG</I>(2, 2) only (Fano partitions) or copies of <I>AG</I>(2, 3) only (affine partitions)or copies of some planes of each type (mixed partitions).</P><P>We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for <I>v</I> = 8 and affine partitions for <I>v</I> = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for <I>v</I> = 14, 16, 22, 23, 28, and an affine partition for <I>v</I> = 18. Using these as starter partitions, we prove that Fano partitions exist for <I>v</I> = 7<SUP><I>n</I></SUP> + 1, 13<SUP><I>n</I></SUP> + 1, 27<SUP><I>n</I></SUP> + 1, and affine partitions for <I>v</I> = 8<SUP><I>n</I></SUP> + 1, 9<SUP><I>n</I></SUP> + 1, 17<SUP><I>n</I></SUP> + 1. In particular, both Fano and affine partitions exist for <I>v</I> = 3<SUP>6<I>n</I></SUP> + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for <I>v</I> = 3<SUP>2<I>n</I></SUP>.</P><P>Similarly, mixed partitions are shown to exist for <I>v</I> = 8<SUP><I>n</I></SUP>, 9<SUP><I>n</I></SUP>, 11<SUP><I>n</I></SUP> + 1.</P>",
	pages = "119-130(12)",
	url = "http://www.ingentaconnect.com/content/klu/desi/2002/00000027/F0020001/05087489"
}