Let F n q be a vector space of dimension n over the finite field F q . A q-analog of a Steiner system (also known as a q-Steiner system), denoted S q (t,k,n), is a set S of k-dimensional subspaces of F n q such that each t-dimensional subspace of F n q is contained in exactly one element of S. Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k = n. In this paper, the first nontrivial q-Steiner systems with t 2 are constructed. Specifically, several nonisomorphic q-Steiner systems S 2 (2, 3, 13) are found by requiring that their automorphism groups contain the normalizer of a Singer subgroup of GL(13, 2). This approach leads to an instance of the exact cover problem, which turns out to have many solutions.

The purpose of this study was to determine the effect of below-knee compression stockings on running performance in men runners. Using a within-group study design, 21 moderately trained athletes (39.3 +/- 10.9 years) without lower-leg abnormities were randomly assigned to perform a stepwise treadmill test up to a voluntary maximum with and without below-knee compressive stockings. The second treadmill test was completed within 10 days of recovery. Maximum running performance was determined by time under load (minutes), work (kJ), and aerobic capacity (ml.kg.min). Velocity (kmxh) and time under load were assessed at different metabolic thresholds using the Dickhuth et al. lactate threshold model. Time under load (36.44 vs. 35.03 minutes, effect size [ES]: 0.40) and total work (422 vs. 399 kJ, ES: 0.30) were significantly higher with compression stockings compared with running socks. However, only slight, nonsignificant differences were observed for VO2max (53.3 vs. 52.2 mlxkgxmin, ES: 0.18). Running performance at the anaerobic (minimum lactate + 1.5 mmolxL) threshold (14.11 vs. 13.90 kmxh, ES: 0.22) and aerobic (minimum lactate + 0.5 mmolxL) thresholds (13.02 vs. 12.74 kmxh, ES: 0.28) was significantly higher using compression stockings. Therefore, stockings with constant compression in the area of the calf muscle significantly improved running performance at different metabolic thresholds. However, the underlying mechanism was only partially explained by a slightly higher aerobic capacity.

We determine the maximum size A 2 (8, 6; 4) of a binary subspace code of packet length v = 8, minimum subspace distance d = 6, and constant dimension k = 4 to be 257. There are two isomorphism types of optimal codes. Both of them are extended LMRD codes. In finite geometry terms, the maximum number of solids in PG(7, 2) mutually intersecting in at most a point is 257. The result was obtained by combining the classification of substructures with integer linear programming techniques. This result implies that the maximum size A 2 (8, 6) of a binary mixed-dimension subspace code of packet length 8 and minimum subspace distance 6 is 257 as well.

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We construct new (n, r)-arcs in P G(2, q) by prescribing a group of automorphisms and solving the resulting Diophantine linear system with lattice point enumeration. We can improve the known lower bounds for q = 11, 13, 16, 17, 19 and give the first example of a double blocking set of size n in P G(2, p) with n < 3p and p prime.