Isolation level for a transaction

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C#

My code as follows.

SqlConnection _sqlConnection1 = new SqlConnection();
_sqlConnection1.ConnectionString = strConString;
_sqlConnection1.Open();
SqlTransaction _transaction1 = _sqlConnection1.BeginTransaction(IsolationLevel.ReadUncommitted);

Now I'm updating a table by using sql command.

SqlCommand _sqlCmd1 = new SqlCommand("Update company set city='TT'");
_sqlCmd1.Connection = _sqlConnection1;
_sqlCmd1.Transaction = _transaction1;
            
int result1 = _sqlCmd1.ExecuteNonQuery();

Without Commiting the transaction I'm creating another connection.

SqlConnection _sqlConnection2 = new SqlConnection();
_sqlConnection2.ConnectionString = strConString;

_sqlConnection2.Open();
SqlTransaction _transaction2 = _sqlConnection2.BeginTransaction(IsolationLevel.ReadUncommitted);

Now I'm updating the same table again

 SqlCommand _sqlCmd2 = new SqlCommand("Update company set city='ww' where city='aa'");
_sqlCmd2.Connection = _sqlConnection2;
_sqlCmd2.Transaction = _transaction2;

From the follwing line it gives a Timeout exception.

int result = _sqlCmd2.ExecuteNonQuery();

Actually my problem is like this. When I opening my program I need to create the InvoiceNo to show it to the user. For that case I'm taking the maximum number from the table and add one to it. In the same time if another user using that program, he should get the next number without repeating the same invoice number. For that case I'm inserting a record to the table when the program loads. And to keep a user is using that record I'm updating a field with '1' with the readuncommited isolation level. If user didn't generate the invoice that updated field is set to '0' and can be used in next invoice by anyone. When user generates the invoice only transaction getting commited. After I set the update statement with the isolation level whole table get locked.