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On some t?(2k, k, λ) designs
Authors:Ryuzaburo Noda
Institution:Department of Mathematics, College of General Education, Osaka University, Tokyonaka, Osaka, Japan
Abstract:t?(2k, k, λ) designs having a property similar to that of Hadamard 3-designs are studied. We consider conditions (i), (ii), or (iii) for t?(2k, k, λ) designs: (i) The complement of each block is a block. (ii) If A and B are a complementary pair of blocks, then ∥ AC ∥ = ∥ BC ∥ ± u holds for any block C distinct from A and B, where u is a positive integer. (iii) if A and B are a complementary pair of blocks, then ∥ AC ∥ = ∥ BC ∥ or ∥ AC ∥ = ∥ BC ∥ ± u holds for any block C distinct from A and B, where u is a positive integer. We show that a t?(2k, k, λ) design with t ? 2 and with properties (i) and (ii) is a 3?(2u(2u + 1), u(2u + 1), u(2u2 + u ? 2)) design, and that a t?(2k, k, λ) design with t ? 4 and with properties (i) and (iii) is the 5-(12, 6, 1) design, the 4-(8, 4, 1) design, a 5?(2u2, u2, 14(u2 ? 3) (u2 ? 4)) design, or a 5?(23u(2u + 1), 13u(2u = 1), 15 4u(2u2 + u ? 9) (2u2 + u ? 12)) design.
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