I. Hetman

collaborators

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9 papers · 1 filter

math.CO2026

Steiner systems $S (2, 6, 226)$ and $S (2, 6, 441)$ exist

Taras Banakh, Ivan Hetman, Alex Ravsky

Via computer search, we found seven non-isomorphic $1$ -rotational Steiner systems $S (2, 6, 226)$ and six point-transitive Steiner systems $S (2, 6, 441)$ , resolving two of $29$ previous…

math.CO2026

There exist Steiner systems $S (2, 7, 505)$ , $S (2, 7, 589)$ , and $S (2, 8, 624)$

Ivan Hetman

In this note two Steiner systems $S (2, 7, 505)$ , two Steiner systems $S (2, 7, 589)$ , and ten Steiner systems $S (2, 8, 624)$ are presented. This resolves two of $21$ undecided cases for b…

math.CO2026

There exist Steiner systems $S (2, 8, 225)$ and $S (2, 9, 289)$

Ivan Hetman

In this note six Steiner systems $S (2, 8, 225)$ and four Steiner systems $S (2, 9, 289)$ are presented. This resolves two of $129$ undecided cases for block designs with block length $8…

math.CO2026

Existence of $S (2, 9, 369)$ , new unitals of order $6$ and other Steiner systems with block length $\geq 7$

Ivan Hetman

Whereas Steiner systems $S (2, k, v)$ with block length $k \leq 5$ have large amount of examples and the existence is established for all admissible $v$ , for $k \geq 6$ only few examples…

math.CO2025

New Steiner systems $S (2, 6, v)$ with block length 6

Taras Banakh, Ivan Hetman, Alex Ravsky

In this paper various Steiner systems $S (2, k, v)$ for $k = 6$ are collected and enumerated for specific constructions. In particular, two earlier unknown types of $1$ -rotational des…

math.CO2025

Enumerations of 1-rotational Steiner systems

Ivan Hetman, Taras Banakh, Alex Ravsky

In this paper new $1$ -rotational 2-Steiner systems for different admissible $v, k$ pairs are introduced. In particular, $1$ -rotational unitals of order $4$ are enumerated.

Steiner systems S(2,6,226) and S(2,6,441) exist

There exist Steiner systems S(2,7,505), S(2,7,589), and S(2,8,624)

There exist Steiner systems S(2,8,225) and S(2,9,289)

Existence of S(2,9,369), new unitals of order 6 and other Steiner systems with block length ≥7

New Steiner systems S(2,6,v) with block length 6

Enumerations of 1-rotational Steiner systems

Steiner systems $S (2, 6, 226)$ and $S (2, 6, 441)$ exist

There exist Steiner systems $S (2, 7, 505)$ , $S (2, 7, 589)$ , and $S (2, 8, 624)$

There exist Steiner systems $S (2, 8, 225)$ and $S (2, 9, 289)$

Existence of $S (2, 9, 369)$ , new unitals of order $6$ and other Steiner systems with block length $\geq 7$

New Steiner systems $S (2, 6, v)$ with block length 6