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FINITE PLANES AND SQUARE DESIGNS
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adder Axiom Baumert-Hall BIBD with parameters biquadratic Bruck-Ryser Theorem cell color Combinatorics construction theorem contains contradiction Corollary cosets cyclic difference set Definition diagonal difference matrix elements entries equation Euler's conjecture exactly once example exists finite projective plane following theorem Galois field GF(pn group difference set group G Hadamard array Hadamard matrix Hence implies incidence matrix integer J. S. Wallis last column last rows Legendre symbol lemma Let G locally maximal sum-free matrix of order maximal sum-free set mod 2k monochromatic Multiplier Theorem nonzero obtain octic residues order 4n orthogonal Latin squares pair of orthogonal pairwise orthogonal Latin permutation plane of order polynomials quadratic residue Ramsey Numbers Ramsey Theory S+HQ SBIBD set in G set with parameters skew Hadamard skew Room square square of side squares of order Steiner triple system STS(v subsystem of order Suppose symmetric Hadamard twin primes Type Williamson yields