R. J. R. Abel

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20152024

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math.CO2024

Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$ , $96$ and $108$

R. Julian R. Abel, Ingo Janiszczak, Reiner Staszewski

We will show that there are at least 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of orders $n = 54$ , $96$ and $108$ . The cases $n = 54$ and $96$ are obtained by constructing s…

math.CO2024

Direct constructions of some group divisible designs with block size $4$ and up to $50$ points

R. Julian. R. Abel, Thomas Britz, Yudhistira A. Bunjamin +1

In this note, we give direct constructions of some group divisible designs (GDDs) with block size $4$ that have up to $50$ points.

Improvements for lower bounds of mutually orthogonal Latin squares of sizes 54, 96 and 108

Direct constructions of some group divisible designs with block size 4 and up to 50 points

Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$ , $96$ and $108$

Direct constructions of some group divisible designs with block size $4$ and up to $50$ points