This basket stitch pattern was published in The Knitted Lace Pattern Book c1870.
In Words
Cast on a multiple of 12 stitches (12 for each pattern repeat and 12 for the selvages).
Row 1 (RS): Knit.
Row 2: Purl.
Row 3: *P8, k4, repeat from *.
Row 4: *P4, k8, repeat from *.
Row 5: *P8, k4, repeat from *.
Row 6: *P4, k8, repeat from *.
Row 7 (RS): Knit.
Row 8: Purl.
Row 9: P2, *k4, p8, repeat from * to last 10 sts, k4, p6.
Row 10: K6, *p4, k8, repeat from * to last 6 sts, p4, k2.
Row 11: P2, *k4, p8, repeat from * to last 10 sts, k4, p6.
Row 12: K6, *p4, k8, repeat from * to last 6 sts, p4, k2.
Rows 1 to 12 form the pattern. Repeat for the desired length, finishing after row 6 or 12.
Charted
Cast on a multiple of 12 stitches (12 for each pattern repeat and 12 for the selvages).
Rows 1 to 12 form the pattern. Repeat for the desired length, finishing after row 6 or 12.