Design theory
Latin squares, their geometries and their groups. A survey
Coding theory and design theory: part II, design theory
Forty-three balanced incomplete block designs
Journal of Combinatorial Theory Series A
A powerful method for constructing difference families and optimal optical orthogonal codes
Designs, Codes and Cryptography
Transversal designs of block size eight and nine
European Journal of Combinatorics
Resolvable Balanced Incomplete Block Designs with BlockSize 8
Designs, Codes and Cryptography
Combinatorial theory (2nd ed.)
Combinatorial theory (2nd ed.)
Truncated transversal designs: A new lower bound on the number of idempotent MOLS of side n
Journal of Combinatorial Theory Series A
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The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: \begin{array}{rcl} \lambda (v - 1) &\equiv& 0\ \mod (k - 1) \\[2pt] \lambda v(v - 1 ) &\equiv& 0\ \mod k(k - 1) \end{array} In this paper we study k=9 with λ=2,4 or 8. For λ=8, we show these conditions on v are sufficient, and for λ=2, 4 respectively there are 8 and 3 possible exceptions the largest of which are v=1845 and 783. We also give some examples of group divisible designs derived from balanced ternary designs.