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In this paper, two new direct construction methods are given for holey self‐orthogonal Latin squares with a symmetric orthogonal mate (HSOLSSOMs). Some new HSOLSSOMs using already known methods are also given. The known existence results for HSOLSSOMs of types 1m u1 and hn are improved; for type 1m u1 there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type hn, there are just two possible exceptions remaining, for (h, n) = (6, 12) and (6, 18). As a byproduct, the known existence results for three holey mutually orthogonal Latin squares (3 HMOLS) are also improved. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 435–444, 2001 相似文献
2.
In this paper, we present several new constructions for k holey mutually orthogonal Latin squares (HMOLS) of type g
n
. We concentrate mainly on k=4; here, for all but two values of n, namely 6 and 15, only a finite number of unsolved cases remain. Some new sets of 5 and 6 HMOLS are also given, in particular 5 HMOLS(2
q
) for q63 or q an odd prime power between 6 and 62, plus 6 HMOLS(4
q
)for q an odd prime power between 8 and 60. 相似文献
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