Further results on optimal (v, 4, 2, 1)-OOCs

Let @F(v,k,@l"a,@l"c) denote the maximum possible size among all (v,k,@l"a,@l"c)-OOCs. A (v,k,@l"a,@l"c)-OOC is said to be optimal if its size is equal to @F(v,k,@l"a,@l"c). In this paper, the constructions and the sizes of optimal (v,4,2,1)-OOCs are investigated. An upper bound for @F(v,4,2,1) is improved. The exact value of @F(v,4,2,1) with v@?201 is given with the aid of computer search. An optimal (24hv,4,2,1)-OOC with h@?{1,2} and v=p"1p"2...p"r, where prime p"i=1(mod6) is constructed recursively. The existence of g-regular (gp,4,2,1)-OOCs for g=3,6,9,16, and p a prime satisfying a suitable congruence is established by direct constructions. Furthermore, the sizes of several new infinite classes of optimal (v,4,2,1)-OOCs are obtained. In particular, @F(v,4,2,1)=U(v) for positive integer v=80,400(mod480).

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