2 problems

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KSWX cyclic difference-family conjecture for prime-power parameters
KSWX conjecture. Whenever $x$ is a prime power, there exists a cyclic difference family with the parameter set $$ and multiplier
Conjectureopencyclic-designs difference-families d-optimal-matricesarXiv posted 2 days ago
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Existence conjecture for D-optimal difference families over abelian groups
Existence conjecture. For each D-optimal parameter set $(v;r,s;\lambda)$ there exists a difference family over some abelian group of order $v$ having these parameters.
Conjectureopencombinatorial-designs difference-families d-optimal-matricesarXiv posted 2 days ago

KSWX cyclic difference-family conjecture for prime-power parameters