Existence of frame SOLS of type anb1

An SOLS (self-orthogonal latin square) of order υ with ni missing sub-SOLS (holes) of order hi (1 ≤ i ≤ k), which are disjoint and spanning (i.e. Σj=1k nihi = υ), is called a frame SOLS and denoted by FSOLS (h1n1 h2n2... hknk). It has been proved that for b ≥ 2 and n odd, an FSOLS(anb1) exists if and only if n ≥ 4 and n ≥ 1 + 2b/a. In this paper, we show the existence of FSOLS(anb1) for n even and FSOLS(an11) for n odd.

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