Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shift in GABA reversal potential (E(GABA)). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (g(GABA-extra)) and experimentally identified, seizure-induced changes in g(GABA-extra) and E(GABA) influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40-100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30-40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing g(GABA-extra) reduced the frequency and coherence of FS-BC firing when E(GABA) was shunting (-74 mV), but failed to alter average FS-BC frequency when E(GABA) was depolarizing (-54 mV). When FS-BCs were activated by biologically based dendritic synaptic inputs, enhancing g(GABA-extra) reduced the frequency and coherence of FS-BC firing when E(GABA) was shunting and increased average FS-BC firing when E(GABA) was depolarizing. Shifting E(GABA) from shunting to depolarizing potentials consistently increased network frequency to and above high gamma frequencies (>80 Hz). Since gamma oscillations may contribute to learning and memory processing [Fell et al., Nat. Neurosci. 4, 1259 (2001); Jutras et al., J. Neurosci. 29, 12521 (2009); Wang, Physiol. Rev. 90, 1195 (2010)], our demonstration that network oscillations are modulated by extrasynaptic inhibition in FS-BCs suggests that neuroactive compounds that act on extrasynaptic GABA receptors could impact memory formation by modulating hippocampal gamma oscillations. The simulation results indicate that the depolarized FS-BC GABA reversal, observed after experimental seizures, together with enhanced spillover extrasynaptic GABA currents are likely to promote generation of focal high frequency activity associated with epileptic networks.