Using recent results concerning tactical decompositions of t-designs with t>2, we make a step forward on the long-standing question about the existence of a simple 3- 16, 7, 5) design; if such a design exists, then its full automorphism group has order a power of 2, possibly equal to 1.
In this paper, we investigate the existence of a super-simple (v,4,9 -BIBD and show that such a design exists if and only if v,4,9 -BIBD and v⩾20.
In this article, we investigate the existence of a super-simple (v,5,4 -BIBD and show that such a design exists if and only if v,5,4 -BIBD and v⩾15.
For each case, we discuss whether such a design exists.
We give construction methods of orthogonal Latin hypercube designs for four factors for any number of runs for which such a design exists by combining smaller orthogonal matrices.
We prove that some vectors are not in, or in a few cases are in, this cone whether a design exists or not.
In this article, we investigate the existence of a super-simple (v,5,3) balanced incomplete block design and show that such a design exists if and only if v≡1,5(mod20) and v≥21 except possibly when v= 45,65.
In this article, we investigate the existence of a super-simple (4,2 -GDD of type gu and show that such a design exists if and only if u⩾4,2 -GDD)⩾4, g(u−1)≡0(mof3) and u(u−1)g2≡0(mod6).
In this paper, we investigate the existence of a super-simple (4,9 -GDD of group type gu and show that such a design exists if and only if u≥4,9 -GDD)≥18 and u(u−1)g2≡0 (mof 4).
In this paper, we investigate the existence of a super-simple (4, 5 -GDD of type gu and show that such a design exists if and only if u≥4, g(u−2)≥10, g(u−1)≡0(mod3) and u(u−1)g2≡0(mod12).
She said she was not even sure if the design existed and talks with a biking firm were in the early stages.
