Although, ashServ.exe sends ping packets to find out if the Internet connection is alive. You can turn this off by checking the "My computer is permanently connected to the Internet" box in the avast Program Settings > Update (Connections) page.
But the IP addresses aren't from avast
IP-Adresses "64.18.25.38"
OrgName: Baltimore Technologies
OrgID: BALTIM-8
Address: 77 A Street
City: Needham
StateProv: MA
PostalCode: 02494
Country: US
NetRange: 64.18.16.0 - 64.18.31.255
CIDR: 64.18.16.0/20
NetName: CYBERTRUSTCIDR
NetHandle: NET-64-18-16-0-1
Parent: NET-64-0-0-0-0
NetType: Direct Allocation
NameServer: NS3.US.BETRUSTED.NET
NameServer: NS4.US.BETRUSTED.NET
Comment:
RegDate: 2001-07-11
Updated: 2005-10-24
IP-Adresses "87.248.218.163".
OrgName: RIPE Network Coordination Centre
OrgID: RIPE
Address: P.O. Box 10096
City: Amsterdam
StateProv:
PostalCode: 1001EB
Country: NL
ReferralServer: whois://whois.ripe.net:43
NetRange: 87.0.0.0 - 87.255.255.255
CIDR: 87.0.0.0/8
NetName: 87-RIPE
NetHandle: NET-87-0-0-0-1
Parent:
NetType: Allocated to RIPE NCC
NameServer: NS-PRI.RIPE.NET
NameServer: NS3.NIC.FR
NameServer: SEC1.APNIC.NET
NameServer: SEC3.APNIC.NET
NameServer: SUNIC.SUNET.SE
NameServer: TINNIE.ARIN.NET
NameServer: NS.LACNIC.NET
Comment: These addresses have been further assigned to users in
Comment: the RIPE NCC region. Contact information can be found in
Comment: the RIPE database at
http://www.ripe.net/whoisRegDate: 2004-04-01
Updated: 2004-04-06